What did the dwarves remove from the cave?
The dwarves found elven weapons in the cave.
The cave is the home to goblins of the mountain that attack Bilbo, Gandalf and the dwarves. Gollum also lives in the deepest part of the mountain, where he keeps the ring of power. Bilbo steals the ring and starts a riddle game with Gollum. He beats Gollum and escapes the caves and catches up with the dwarves. Gollum will later venture out of the cave to find Frodo and his precious.
Bilbo got the gold the dwarves promised, goes back to the shire, and puts the ring he found in the cave where he met gollum on his mantel. Bilbo goes back to his little hobbit home with the ring he found while trying to escape the goblins in their cave after earning the eternal gratitude of the dwarves, elves, and humans.
Yes, the wizard(Gandalf) likes Bilbo very much. It is by the will of Gandalf that Bilbo comes along with the dwarves for the quest. His concern for Bilbo can be seen when all the dwarves come out from goblin's cave but Bilbo remains behind. Gandalf continues to visit Bilbo even after the end of dwarves quest.
Smaller than a regular star. Please note that there are different types of stars called "dwarf star", with quite different sizes: red dwarves, white dwarves, brown dwarves, white dwarves, and the hypothetical black dwarves (which are not expected to currently exist). White dwarves (and black dwarves) are the smallest of these, with a size about as big as our Moon.