If you are so keen on investigating walruses in zoos, you could check what helps breeding and avoiding tusk damage, something which is poorly known. Tusk caps are rather an emergency / veterinary measure.
Soft-bottom pools, large pools and pools with gentle sloping exit were suggested to help protecting tusks of walruses. Also, it would be interesting whether in recent years more walrus have tusks than in earlier years (a progress is being made)? And at what age males and females breed, and is there a link to larger group size?
This topic is one that is frequently asked about but with no real conclusive data behind the discussions until now. Every aspect of it is interesting and worth learning about -- tusk caps included.

(Regarding your other query, I also made a rather extensive post only a day or two ago detailing a few of the efforts that have been attempted and proposed to improve reproduction, but it's definitely something I'd like to discuss more in depth here later on).
Tusk caps are not always applied on an emergency basis -- they're often used as early as possible with calves to prevent tusk damage, to keep them from being ground down, and to keep existing damage from becoming infected. Veterinary, yes, but a critical aspect of the topic.
Environmental altercations, as stated before, have had limited effect due to walruses destructive nature. Habitats lined with soft materials have been attempted (and destroyed), but I'm not certain about substrate use -- this may have been in use at Hagenbeck and Harderwijk, can anyone confirm/deny? That would be fascinating!
I'm not sure how effective these habitat modifications have been, I'd definitely love to see any data available on this (I only know that in parks where these efforts are present, tusks are still being damaged and extracted). If I were to give my opinion, it seems to be largely, or at least significantly, individually behavioral -- the same parks that have animals with pristine, exemplary tusks
always have animals raised alongside them or in the exact same environment that have required extractions, or otherwise extensively damaged their tusks. Tusk damage and removal also occurs at an incredibly higher rate in cows compared to bulls, and I'm not sure why. I will definitely be asking about this!
As for your last questions, both bulls and cows will most commonly conceive their first offspring at age 10 -- the youngest cow to conceive was 6, and the youngest bulls sired offspring at age 9. Spermatogenesis in bulls has been documented as beginning at age 5 in one instance.
I'm not sure if there's a tangible link to larger herd size and increased reproductive success, though this is certainly natural and strongly promoted among modern breeding facilities -- parks with larger herds have had more calves conceived, but this comes with the territory of having more cows to produce said pregnancies. Several of the most successful parks in the world have only housed breeding pairs, and the most widespread and reproductively successful (and consistent) walrus lineage in the world today originated from a single breeding pair which was self-enclosed without outbreeding for three generations until the founder bull died.