Water Deer - Tusk Construction & Eruption
Canine construction
Teeth are composed of two parts, the root and the crown, the latter section being that which protrudes beyond the gumline. To the best of my knowledge, the minutiae of tusk development has only been studied for a handful of mammals and we don't know what triggers their eruption in most species, including water deer. In dugongs, we now know that a substantial elevation in testosterone is the trigger, and if canine development is indeed associated with the same pathway as antler formation as Heckeberg postulates, a similar mechanism may be at work in water deer.

Again, as with the spark for their growth, there appears to be very little data on the micrographic structure of water deer canines. We know that most of the crown is composed of dentin, protected by a thin coating of enamel towards the tip, although this can be worn away. In their 2021 paper to the Proceedings of the Royal Society B, Harvard University zoologist Megan Whitney and colleagues note that, owing to the geometric constraints of producing enamel and dentine continuously, the dentine core isn't completely covered with enamel in ever-growing tusks as it is in other teeth. Instead, an enamel cap is present initially at eruption that's eventually worn away, leaving a tooth consisting mainly of dentine with cementum coating the root.
Quite how the tusks are protected from the elements outside the mouth, given that mammal teeth typically require the controlled moisture, temperature and pH conditions within the mouth to prevent drying out and limit dental disease, remains a mystery. Assuming, however, that water deer tusks are structurally in line with those of other mammals, and when shown a few my dentist commented that they felt very much like ivory, we would anticipate collagen fibrils to form a meshwork between dentinal tubules within the dentin. These fibrils are typically located in two planes, an arrangement different to the single plane set we see in other teeth, and which helps to strengthen the tusk by dissipating inflected mechanical forces and hampering crack formation. Hokkaido University veterinarian Alireza Nasoori provides an excellent overview of mammalian tusk biology in his 2020 paper to the Archives of Oral Biology.

Nasoori points out that generally a tusk's crown is almost devoid of cells, making cell damage and inflammation less likely in the event of trauma. Furthermore, the dental pulp, the living connective tissue in the centre of the tooth, makes up a proportionally small area that's well separated from the edges. In part, Nasoori explains, these features may minimize the sensitivity of tusks to touch and, more importantly, pain. In elephants, for example, the distil two-thirds of the tusk pulp has very poor innervation, suggesting pain signals are poorly relayed.
In addition to the potential for reduced sensitivity in the tusk itself, the size of the socket (see: Freedom of Movement) and its associated ligament may assist in dampening the force of impacts arising during fights. Finally, the handful of mature skulls I have observed displayed some growth of trabecular bone in the sockets behind the tusks. I assume this is the 'closing of the cavity' that Robert Swinhoe mentioned in 1873, but logically this may also act as an impact-dampening "cushion" of bone, similar to that we see in deer antlers. There does not appear to be any special adaptation of the skull itself to accommodate such impact. In 2017, for example, Jinwoo Oh and colleagues studied the skulls of 35 Korean water deer and found no significant difference in the closure rate of the cranial sutures (i.e., the fibrous tissues that unite the bones of the skull and are ossified as an animal ages). The researchers point out that this is interesting because we'd expect the sutures to remain open for longer in bucks than does, to help absorb the forces generated during the rut.

Of course, it may also be the case that the forces are less than we assume, given the tusks are sharp, damage is typically to soft tissues rather than tusks connecting with bone, and the impact isn't directly proceeded by a running collision as it is in, for example, sheep.
Tusk eruption and development
The process of tooth formation in mammals is complex and the trigger(s) for their eruption (i.e., the point at which they begin to push through the gum) remains largely unknown. Among the deer, we have a good understanding of the tooth eruption sequence for most species, but their initial development and the catalyst for eruption is, to the best of my knowledge, unknown. Under the assumption that the process follows what we currently understand of the general mammalian scheme, the tusks will develop via a budding of the connective tissue within the mouth, and this probably gets underway in the embryo. They may erupt through the gum via a combination of tusk growth and the shrinking and cross-linking of the collagen fibres in the periodontal ligament (see: Wikipedia - Tooth Eruption for a more detailed explanation of this).
We do know that water deer tusks grow rapidly from the open hollow root, initially within the large sockets. According to data collected on farmland over three consecutive winters and provided to Arnold Cooke by Cambridge-based deer stalker Martin Guy, the tusks rarely erupt before the bucks are at least five months old. Indeed, the average length of the canines, from tip to gum line, was only 1 mm (0.04 in.) during November. That said, in his 2019 book Water Deer and Muntjac, Cooke does note that one juvenile buck found dead on farmland in October 1977 had erupted canines, suggesting that they may occasionally erupt before mid-winter.

Guy's data suggest that once initial eruption has occurred, the canine lengthens quickly, the average length of exposed tooth increasing to an average of 17 mm (0.7 in.) by late December/early January and to 25 mm (1 in.) by March. It's shortly after this, during April/May, when the bucks are around 10 months old, that they begin to protrude below the upper lip and become discernible in the field. Where close observation is possible, such as under captive conditions, there is some suggestion that tusks can be detected as early as late winter, when bucks are only around six months old.
According to Childerley's data, this rapid increase in size is initially a reflection of an increase in protrusion, the tusks being similar lengths at the end of November and end of December (around half-grown), followed by a rapid lengthening and increase in curvature. Once the animal is 14-18 months old (e.g., around the end of the following August/September) the base of the tooth begins to fill in, taking on a more rounded shape as the root begins to close. It appears from the observations of both Arnold Cooke and Paul Childerley that growth of the tusk after about two years is in the thickness of the root only. Indeed, writing in 1872, Victor Brooke noted how the canines, as they attain their maximum development, contract their pulp cavity to the point where it is obliterated in old bucks, while at the same time there is a gradual protrusion of the root of the tooth. Consequently, old bucks may present with chipped and broken tusks, which protrude only a centimetre or so from the gum, but with very thick roots. Certainly, damaged and even missing tusks are not uncommon in mature animals and, writing to Robert Swinhoe in 1871/72, Imperial Customs officer Howard Russell confessed that, given how often he found tusks to be damaged or absent, he initially thought they were deciduous until he examined the root of an extracted tusk.
There is considerable variation in tusk length, with 80 mm (3 in.) widely cited in the literature as the maximum exposed length (i.e., from the tip to the gum). At Whipsnade Zoo, where the overall body size of water deer is comparatively small, tusk length was found to average 44 mm (1.7 in.) during the 1990s, while Arnold Cooke, in his 2019 book, notes that those in Cambridgeshire farmland averaged 48 mm (1.9 in.), China averaged 53 mm (2.1 in.) and bucks at Woodwalton Fen came in at 60 mm (2.4 in.), the maximum being 72 mm (2.8 in.). Tony Dalby-Welsh of the International Council for Game & Wildlife Conservation's UK Trophy Evaluation Board told me that the largest tusk measurements recorded in the UK were from a buck shot in Bedfordshire during 2013. The "CIC score" for this Gold Medal buck was 272, made up of lengths of 105mm/104mm (ca. 4.1 inches) and the greatest circumference of each tusk being 32mm (1.3 in.). These tusks were 4mm longer than the next highest scoring buck, the circumferences of which were also 32mm.

The root comprises an additional 1.5cm (0.6 in.) or so of the aforementioned canine lengths and in mature individuals the cervix, the juncture between the root and crown, is sometimes visible as a dark line running parallel just below the gum. Based on data given by Todd Wheeler in his chapter on sabre-toothed cats in The Other Saber-tooths: Scimitar-tooth Cats of the Western Hemisphere, published in 2011, the periodontal ligament covers about 17 mm of the root, which is around 21% of the total length of an 80 mm canine (24% of a 70 mm or 28% of 60 mm canine), which in turn suggests that, in mature bucks, 70-80% of the tusk protrudes below the gumline and 60-70% below the top lip.
When considering total tusk length (i.e., the length around the outside curve of the tooth), in their account of Hydropotes for the fourth edition of the handbook Mammals of the British Isles, Cooke and Lynne Farrell give a range of 81-95 mm (3.2-3.7 in.), the average being 87 mm (3.4 in.). The tusks of mature bucks are 10-12 mm thick (0.4-0.5 in. front to back), although some do occasionally present larger, and I know of at least one animal from Bedfordshire, shot in February 2021, with tusks in good condition and of average length but that measured 15 mm (0.6 in.) in width. Similarly, in their 2013 paper to the Journal of Veterinary Medical Science, Yungkun Kim and colleagues include a photo of the skull of a water deer buck from Korea with a similarly thick canine. In such cases, the inside edge is noticeably straighter than that of narrower tusks. I have no equivalent tusk size data from Norfolk, Suffolk or Buckinghamshire and would be interested to hear from anyone who does.

According to the requirements set out by the Council for Game & Wildlife Conservation United Kingdom Trophy Evaluation Board (CIC UKTEB), to qualify for the lowest level of "medal" (i.e., bronze) a buck requires a canine length of at least 65 mm (2.6 in.), with a circumference of 25 mm measured at the largest circumference of the tooth's diameter.