- all a bit boring and just random depending on where you sit

yes

no.

yes if you like although probably too easy if people don't care about
the bridge result - it's probably not too tough to organise to trump
your own side's ace

sorry all of these are a bit dull

yes

no

yes

I also prefer prizes that involve some small level of skill rather
than just depend on what you are dealt.  How much you want them to
'interfere' with normal bridge is us up to you.  Other possibilities
that may be harder to win are:

Last trick made up of one card from each of the four suits
Bid and make 5NT

The difficulty with a lot of these is that they are too easy for table
to collude in at the cost of totally silly results.

Alternatively you could have a range of things people need to do, and
have them each draw them from a hat secretly, so that others don't
know what they are trying to achieve (or they may have to be
partnership ones).  When you make your target you call the TD and get
your prize, showing your slip.

So many of the same items e.g. redouble, win a trick with a non-trump
7, ruff partner's winner would work.  Or

- a trick made up of 4 cards in order (7-8-9-10 say)
- have an auction starting 1C - 1D - 1H - 1S - 1NT (plus any number of
passes)
- take a successful finesse against a card no higher than the 7