Ah crap, I responded to you like an hour ago but the blockchain ate it.

1. Yep - it's part of the get_dynamic_global_properties API call as total_vesting_fund_steem. This number is also shown on both steemdb.com and steemd.com (in the right columns).
2. Yes, it continues to grow. If you just refresh the page on one of those sites after a minute, it'll probably increase before your very eyes.
3. There are some built in mechanisms to grow each account's vests along with the inflation. I don't have exact numbers or a great explanation for it - but there are some protections built in.