Can shadow cat or any other character with phasing or flying pick a character up (without breakaway) and carry him to another location. Also can you pick more than one character up in one turn. I really need to know this.

Yes. A character with Phasing and flying can carry a character without making a breakaway roll, as per the Phasing power.

No, a character cannot carry 2 figures in the same turn.

Yes, any flying character can pick up another character and carry them. The flying character has to be adjacent to the character before any movement, and the character being carried is put down adjacent to the flying character when the flyer stops moving.

The flying character must roll breakaway if it is adjacent to an opponent. If the carried character is the only one adjancent to an opponent (ie - between the opponent and the flyer), then no roll is needed.

A flyer can only carry one character at a time, and only one in a turn.

Flyers can use their superpowers, so Shadowcat can phase while carrying someone, or Vulture can Charge while carrying someone, etc. The only one I thinnk that doesn't apply is Hypersonic Speed -- Supes can't carry someone and Hyper-fly.

Hope this helps.

Just to clarify, a character with only phasing (not a flyer) can not pick up another character. Only flyers (and Sentinels and Sinestros) can carry another figure. A character with phasing AND flying can pick up an adjacent friendly figure without breaking away.

And no, you can only pick up one character (adjacent to you at the beginning of your move) and drop him/her off on an adjacent square at the end of your move.

Thanks everyone. I got into anargument about this yesterday and now I can show him. One more question if you dont mind.....

Can a character use flurry with bcf or can a person charge and use bcf?

Yes to both combinations.
Both Charge & Flurry allow you to use any close combat attack and B/C/F does not have any restrictions on being combined like CCE or RCE have.