In the cloud city scene when Luke is sliding through those tubes, is that his hand that we see falling below cloud city?

Doubtful. his hand falls first and waits a while before he falls. Most likely it's just debri.

I've wondered what this was for years...I don't know if Lucasfilm has ever given the definitive answer. I spent a number of years thinking it was maybe Luke's lightsaber - but looking at it now on a bigger TV screen, it's too big and square to be either Luke's hand or his lightsaber.

It's something that falls off Luke's belt, his wallet or sunglasses maybe.

Condoms. Remember, at this point, Leia was fair game, or so he thought. Then again, it could have been some of that beef jerky he had on Dagobah.

Could have been his Pistol... Maybe his lightsabre... The image is very quick and indistinguishable...

Lightsaber flew off with hand. So doubt it's that.

In the Zahn trilogy:

I think it was his blaster, as it seems to appear after he hits that antenna thing and gets jerked to a stop

Oh god

Probably Wampa remains.

and name it if I remember correctly

Good Call!! Those books are awesome. Anderson's books after Zahn are okay but I much prefer Zahn's story telling.

And for the person who said "oh God" to this post. You should read the books, they are great.