Traveling around Cantha

I just bought Factions, so I don't understand the story much. But I read that at one point in the campaign, the path splits up based on alliance. If you choose one alliance, can you travel to areas on the other side?
Let's say I ally with Kurzick. Can I:
-go capture elite skills exclusively in Luxon territory?
-buy Luxon armor?
-enter Luxon PvE missions?
... among other things?

Yes. You will need to complete the other "Befriending the Luxon" quest to complete the other side of the campaing, and to have more Luxon Faction Points (not in the title) if you want to be able to use Luxon Merchants, Luxon Weapon Crafters or Luxon Armor Crafters.

Which side you pick isn't really perminant, nor does it have any real negatives. Much like assigning attributes or skills, GW is very forgiving and you can change things around at any time and play for either side if you want to. Also, you HAVE to complete both sides if you are trying to get the protector of cantha title, as each faction has an exclusive mission available only to them.

This is the biggest downside of the aliancesystem. We are talking about unspend alliance points here...

So when you want to craft Luxon armor or buy Luxon keys, etc then you need to have more unspend luxon points than your kurzick points, otherwise those crafters dont want to talk to you.

But some town/outpost can be controlled by enemy alliances. The alliance who owns a town/outpost plays a big role too... luxon towns often are controlled by a kurzick alliance (and visa versa). For example: when you want to buy something in a luxon town/outpost that is controlled by a kurzick alliance then you need to have more unspend kurzick points than luxon points.

you can do whatever the hell you want

I read about Moebius Strike, and it said something about being unattainable to Assassins allied with Kurzicks. That's why I wanted to know what else is missable.
I don't understand this at all... I guess I have to play this part of the game to understand it.

It's simple, really.

Which faction you prefer only matters to the game by the issue of which faction you have more of - if you have 500 kurzick faction and 100 Luxon, you'll be treated as a Kurzick. This means that the luxon NPCs won't be willing to trade with you. As soon as you spend the faction, things change.

A different matter is the Faction system that won't let you access areas until you progress far enough in the storyline. This just means that to access all of the Kurzick lands, you'll need to complete the befriending the Kurzicks quest, which means earning 10000 Kurzick faction. Vice versa for Luxons. Doesn't take long.

You should be able to bribe all Factionites the way you can their Priests, guess it fits with the game with most monks being money hungry though lol

many people get confused by this whole "allied with a faction" thing. So let me give you a few pointers.

1. You don't "become" Luxon or Kurzick when you choose a side. You are simply "allied" with either one.

2. More specifically, you Guild is allied with a particular side. You, personally, don't really ever choose a side.

3. As you travel through one side or the other (Luxon or Kurzick), you will naturally accumulate Luxon or Kurzick points. These points can be "spent" by donating them to your Guild/Alliance, or buying jade/amber, etc. As you travel through a territory, the various NPCs will only talk to you if you have more of their "unspent" faction than you have of the other. For example, if you have 2000 Luxon faction and 3000 Kurzick faction, the Luxon NPCs will not talk to you. This is not affected by your Guild's alliance. You can travel through either territory whenever you want and do any and all missions, and capture elite skills on both sides.

4. Even if you have more of one faction than the one for the territory you are in, you can bribe the Priests at the rez shrines anyway, so you can accumulate their faction.

5. In order to do both sides fully, you will need to do both the "Friend of the Luxons" and "Friend of the Kurzicks" quests. These will each require you to get 10,000 (unspent) of the appropriate faction. Once each quest is completed, you can spend the faction. The side your Guild is allied with has no affect on this either.