Howdy, welcome to the Matrix and all that malarky.
Unfortunatly i'm no the best person to answer this as when i started i didn't have a clue what was going on either, but asking around is always a good idea, people were very helpful to me.
Also, there is a guide section in this forum that has lots of info and stuff on it, don't know about any other types of guides, cause as i say i just jumped into it also never having played one of these things before.
As for playing in zion, unfortunatly...or fortunatly depending on your point of view (Zion was a tad dull in the films to be honest) you can't at the minute, the loading area is as close as you get, but the Matrix is a much bigger place than you might think when you first start with lots to see and do, what with those 4 districts not to mention the constructs you can visit.
And currently we are on chapter 9 and when you get your critical missions and get involved in the story you'll be on the same page as everyone else. But to find out more of the backstory and whats gone before etc. you can buy archive missions from archive vendors that lets you catch up on the story and gives pretty good xp too

As well as looking at old live events on these here boards to keep you up to date an all.
As for the not being able to fight, think that might be an annoying bug, or maybe your weapons broke or something...not sure, have to get more info to find out, sorry.
Anywho, hope that helps a bit...Have fun!