Just got done with a Skype demo session, which was a lot of fun with a fair degree of silliness as well.
As for OP's questions:
1) The game was very quick and fluid; it would have taken us two or three sessions in Saga Edition to accomplish what we did in one with EotE, but as for "the feel of Star Wars," that's a tough one. Things do happen very quickly, and there is a lot more narrative control, though I'm sure our group will get better with action embellishments as we get more used to the system. Beyond that, replicating the "galaxy far, far away" is pretty independent of system, having more to do with the sorts of adventures your GM is running and what backdrop elements he includes. For our group, we started out in Mos Eisley, in Chalmun's Cantina (the one from A New Hope), with a quick combat before heading out into the Dune Sea to fight some Tusken Raiders, so it certainly had the feel of Star Wars to me. With combat being much quicker and more open to creative interpretation (especially with Advantage and Threat), there's more chance for immersion and less having to worry about tactical aspects.
2) I think the rules do deliver on the fast, exciting action. As noted above, combat were quick (granted, we were only fighting minions and a couple of us rolled really well on our attack rolls, generating enough Advantage to score crits and take them out instantly). The only real delay was for those people without the sticker'd dice or the dice app converting their regular dice results to those on the chart to get their final result, with one player having to do her difficulty dice and skill dice separately due to not having a way to distinguish dice colors on the app she was using. But towards the end of the session, they were getting much quicker about it, with the only big drag was trying to figure out what their Advantage points could be used for.
3) Character creation is hardly limiting at all, as you've typically got a lot of points to spread around on skills, raising characteristics, and buying talents. I played a Human Smuggler Scoundrel/Thief/Force Exile that was almost a straight conversion from an old D6 character that I never got to play. Character would have been grossly difficult to build under OCR/RCR, and far more powerful than intended under Saga Edition. The other characters were a (busty) female Twi'lek Bounty Hunter/Gadgeteer, a Trandoshan Hired Gun/Marauder, and a Human Smuggler Pilot/Scoundrel. Each of us had our specialties, and could contribute equally in most circumstances. There wasn't much exposure to social combat (though I did manage to get us banned from Chalmun's Cantina due to rolling lots of Threat on a Charm check against an NPC whose bacon we'd just saved). I would dare say that outside of D6 Star Wars, which barely had any restrictions on character creation at all, this has very few hard limits; if you can think of a character concept, you can build it. Still, I would have liked the starting selection of races to have been a little broader (Duros and Zabraks being the two races I most miss), but you can do a lot with what there is.
4) Given that combat is abstract, I'd say it'd carry over to play-by-post quite well. In fact, over at the D20 Radio Forums, there's actually an EotE PbP game that's in the formative stages, but you'd need to be a member of the forums in order to view it (it's in the members-only gaming boards). So the only issue you'd really have would be the one common to most PbP games, that of interest fading due to lack of timely posts from everyone.