Since big figures move per standard rules of flight, does that mean that they can carry figures as well?

Yup, they can carry a character. Funny, when you think about it: the Sentinel (or Sinestro) can carry one friendly chracter, per the normal flier rules, but it can also carry two captured opposing characters

Can all big figures capture or is it simply a Sinestro/Sentinel power?

It is not an ability possed by all Big Figs, no. You'd have to check their specific rules to be sure, but I think that Sentinel, Sinestro, and Dark Phoenix can capture, while Galactus, Spectre, and Jean Grey Phoenix can not capture.

One more question, if a big figure is adjacent to an opposing figure, can a big figure use ranged combat attacks against an opposing figure that is not adjacent?

Again, not necessarily. From the Icons rule book (page 31, under 'Big Characters'):

BIG CHARACTERS
A character with the damage symbol is a big character. Big characters are colossal, and they may have special rules that are provided with the figure. Big characters do not halve their range values when attacking soaring characters. All big characters block lines of fire to other characters. Big characters ignore the effects of hindering, elevated, and outdoor blocking terrain on movement. Big characters cannot be moved by Telekinesis.

Not a whole lot there, eh

Bottom line, individual Big Fig rules can vary quite a bit, so it is good not to make sweeping statements; instead, if you have questions about a particular Big Fig, check its rules.

That said, without paging through all of them right this instant, yes, I do believe that all the current Big Figs may shoot out of adjaceny. But if you are specifically wondering if, say, Jean Grey can do that, I'd go check her rules before planning your strategy around it.

You should have said, "the Sentinel (or Sinestro) can carry one friendly character comfortably, per the normal flier rules, but it can carry two captured opposing characters very uncomfortably."

Oh, I don't know... you ever been captured by a Sentinel? Maybe the captured figs get to ride in style

It'd be cool if they had big pockets to put the captured mutants in...

Hey, hopefully we'll get to see Sentinels in battle next weekend!