Ok, so let's say I want to run a swarm team of cheap figures and/or pogs that completely surround my opponent to stop them from going anywhere, until they kill some of the figures surrounding them.

Firstly,

When you attempt to break away, it's all or nothing, right? If you are based with four opposing characters, you only roll once, and if you succeed, you ignore all four characters for movement when breaking away, right?

Secondly,

Is the only possible way to completely "box in" a character to surround him with 8 pieces? Or could he still break away and move through the occupied squares to break away?

Thanks in advance.

Yes breakaway is all or nothing. One roll.

Unless you have a power or ability that allows you to ignore characters for movement purposes, you cannot move through a square occupied by an opposing character.

That's correct.

If he can use the Flight ability or has some other way to move through squares occupied by opponents he woon't be stuck, but otherwise, he will be.