Can character jumps or swims?

They can jump and you can see that in the introduction to the game. When the nord jumps off the rock from 3-5 minutes in. It is an MMO and and ES game and you have been able to swim and jump in most of those. You shouldn't worry about this, it is almost guaranteed to be in the game.

From videos we have seen so far, yes and yes.

there was a video somewhere that showed 2-3 characters in the water, so im sure swimming is in the game, and i almost wanna say one of the characters jumped into the water and landed by the other 2, so that would confirm that there is jumping as well, just youtube elderscrolls online footage, there isn't much to look through, so you should be able to find it fairly quick.