1) If everyone earns the same minimum base, why wouldn't individual purchasing power decrease as prices increase for goods, services and rent?
You mean as a matter of regular inflation? Presumably the base should periodically increase to account for that. I think that's how most welfare programs work.
2) How exactly does one set the fair handout value of the UBI? Lowest common denominator for sustenance, highest wellfare provided?
Does it vary by region/state? (eg: 1000 USD in NY will not get you a lot, but can be enough for a remote place in the countryside).
There's a wide variety of proposals out there based on different goals and principles. I think a reasonable policy would vary by region based on actual living costs. $1,000/month is enough to live well in Alabama. In California, there are homeless people living on the same amount.
Andrew Yang's proposal is just for a flat $1,000/month payment for all US citizens.
3) How 'universal" is it? Would it be distributed to "all" people? Whats the criteria exactly?
It varies by proposal. This is the conventional definition as I understand it:
A basic income is a periodic cash payment unconditionally delivered to all on an individual basis, without means-test or work requirement.
That is, basic income has the following five characteristics:
1. Periodic: it is paid at regular intervals (for example every month), not as a one-off grant.
2. Cash payment: it is paid in an appropriate medium of exchange, allowing those who receive it to decide what they spend it on. It is not, therefore, paid either in kind (such as food or services) or in vouchers dedicated to a specific use.
3. Individual: it is paid on an individual basisand not, for instance, to households.
4. Universal: it is paid to all, without means test.
5. Unconditional: it is paid without a requirement to work or to demonstrate willingness-to-work.
https://basicincome.org/basic-income/