The website of BetaBatt themselves is very sparse: not more than a single announcement and an email address. It contains just enough information to be of some interest to investors, so there simply isn't much to go on.
However, I think I can answer some of your questions. Provided the battery is sealed and does not leak, it is safe for users. Tritium is radioactive, but the energy it emits is very 'soft' in comparison to that emitted by other isotopes. Only by cracking open the container and then swallowing the contents would you be in danger, but my data tables indicate you would need to ingest or inhale (there is no difference here) quite an amount of tritium (1.1 GBq) before you are exposed to the maxium yearly dose of 20 mSv. It might be a problem for children and pregnant women, since the maximum allowed dose is much smaller for them.
The site itself says that the first types are expected to reach a power output of 400 microwatts per cubic centimetre of battery volume. It depends on the properties of the silicon how much amps and voltage this translates into: I literally have no idea how to calculate that. However, the 400 allows me to estimate the amount of activity in that volume: between 1,5 and 2 GBq. So you would have to be quite careful with a cracked battery, and in fact have a nasty problem on your hands since it is illegal to throw it away just like that.
In other words, only BetaBatt and/or a few select subsidaries are probably allowed to recycle the batteries: it is just a matter of opening them, withdrawing the tritium (most likely in the form of water), concentrating it to desired activity and filling a new battery with the concentrate. There is no toxic waste product to deal with: the tritium decays into inert helium. You of course have to allow for a little room for the helium to expand into since it is a gas. A rough calculation informs me that after 1 half life, you would need about 0,3 cubic centimetres per cubic centimetre of active battery to maintain atmospheric pressure. It is quite easy to construct a metal case which can withstand higher pressures, so the expansion volume can easily become a factor 10 or so smaller. (In fact, regulation probably stipulates that the case already be tough to resist accidental cracking, killing two birds with one stone.)
Price? Hard to say, but it will not be cheap.
I like this invention quite a lot: I'm sure that BetaBatt will also see plenty of opportunity to market a new and vastly more efficient type of tritium detector. Because of the low energy of emitted radiation, tritium is hard to detect; this device has to be very efficient in capturing the radiation, and thus simultaneously in detecting it.