If you attach four walls to a bed and put the sechach on top, it is kosher. Reb Yehuda says since a succah has to be strong, if it can’t stand by itself, it is possul.

A succah must have more shade than light, if the sechach is thick enough so that you can’t see stars through it, it is still kosher.

Succa 2:3

If you build a succah on top of a wagon or on the deck of a ship it is kosher and you can go into it on Yom Tov. If you make the succa on top of a tree or the back of a camel, it is kosher but you may not go in there on Yom Tov. If one wall of the three walls of a succa is attached to a tree, the succa is kosher but you may not go in it on Yom Tov. If three walls of a succa are not attached and the fourth one is, then you may go in it on Yom Tov. The general rule is, if it can stand without the tree you may go in it on Yom Tov.