Absolutely. I did quite a few of these with BA deal a few years back. I sleep on the plane, so am refreshed and ready to go the morning of arrival. Its pretty much like taking transcons here in the US.

Yes, often

Why not?
 

I don't sleep at all on aircraft (well, not in Y anyway!) but 3 days in New York would sound perfectly reasonable to me (I'm UK based). As it happens, I'm off to Denver for a 4 day weekend next month, 2 days of which will be spent in the Rockies doing a *lot* of walking and the rest shopping and eating round Boulder. Can't wait. Admittedly we're in J this time though (and the wife is very excited, it's her first time in business class). Paris for 3 days sounds fun, is about the right length of time. Go for it.

I live in Southern California and routinely go to visit my family in Scotland over a weekend; typically leaving LAX on Thursday and returning on Sunday. Not a big deal at all and very practical :-)

Seems a little odd to me, but if I was on the east coast I'd probably consider it. I've done stop-overs that only lasted a couple days each. On the way from BKK to JFK, I stopped over for a couple days in NRT. Then from MUC to ORD I stopped over for a couple days in LHR. It's fun to hang out in another country, even if it's only for a couple days. Environmental impact is really high though for such short trips, especially if you make a habit of it.

to each his own on all these but to most on this board a big yes to all three.

Going for a four day weekend to LHR this weekend, normally do three days.

I save my big vacation time for trips that are generally very difficult to get to, so that does not leave a week's time for a trip to Europe, so we do a lot of three/four day trips.
FWIW, I don't sleep much at all on a plane.