Envelopes!

For question #1:

I can't see any way to maximize your expectation, unless you can make some kind of reasonable assumption about the range/distribution of possible values.

For me personally, I'd probably choose some value Y which I'd be satisfied with. If the envelope I pick has more than Y, I stick, otherwise I swap -- no regrets either way.

Unless, of course, he's kind enough to tell you how much money's in the unopened enveloped. That would make your choice much easier.

PP