The effective duration of the varicella vaccine isn't well known at this point, various studies however have suggested that immunity can last for 10-20 years post vaccination, particularly where two doses are used. It's possible that it may well last longer than that (live-virus type vaccines often provide lengthy immunity) although it can be boosted using the single antigen vaccine if required.
With the vaccine not being mandatory in the UK (and hence the proportion vaccinated not hitting the herd immunity threshold), does vaccination risk putting the average age of infection up (i.e. predisposing to more serious infections as an adult)?
We'll know better when the vaccine has been in use longer - so it can be determined how long it remains effective. The indications so far are that it retains a fairly stable 80-85% effectiveness. If there is a significant drop off in effectiveness then I imagine there will be calls for boosters to be scheduled - chickenpox is often more serious in adults.
Does the vaccine protect against shingles in the long term?
Shingles occurs when the dormant varicella zoster virus from a prior infection (i.e. chicken pox) "wakes up" and you get shingles (and all the associated "fun") - so if you're immunized against varicella and don't get it then you are protected from shingles. However the varicella vaccine is not 100% effective, and it's possible that a vaccinated person can still get the disease - although this is generally a much milder experience (in fact it's possible to contract the disease and not even know it), which is a double-edged sword since while it's reducing the chances of getting it and the severity if you do it leads to the possibility that a vaccinated person may believe that they have never had varicella and therefore believe that they aren't susceptible to shingles.
For older people (50+) there is the option to get vaccinated for shingles specifically (Shingrix) and before giving this you should be tested for immunity to chickenpox and if not you should be directed to that vaccine instead.