My viewpoints/memory on these:
1) Will the two other books be 'compatible'? Even if they are the same rules, can a Rebel, Smuggler and Jedi all party up? Asking because I know my party is going to want to go in different directions.
FFG has stated the systems are intended to be compatible and the systems will use the same dice. The presumption is that they will use a format similar to the WH40K product lines. I haven't played these games, but from what other players have reported that, while they are compatible, they don't mesh well. Hopefully the Star Wars products will work together better than 40K does (closer thematically, less massive differences in power levels in each product) or they'll use a different format to support compatibility.
Bottom line, though, is there have been absolutely zero official comments about how they games will be compatible beyond that they are intended to be compatible, and they'll use the same dice.
And even if there had been official comments, they haven't even released the first product yet. IMO its important that remember that there's very little that isn't subject to change about the later games at this point. Even "official" statements probably wouldn't be very reliable indicators about what we can expect to see in the later product.
In fact it just might be the reason why none have been made.
2) Will they release a beginner box for each book […]?
I really doubt this is gonna happen. I think if you consider what you get in the EotE Beginner Box ("BB"):
A full adventure
And with an MSRP of $29.95! This isn't typical of FFG's pricing strategy at all. I mean, MSRP on the dice alone is $15. Take into account the time and effort it took to produce the Beginners box (art design, rules adaptation, editing, etc), it's highly unlikely that the profit margin on the BB is anything like the their 'usual' products. Their adventures for WFRPG seem to be priced around the same $30 point, and I think you get less (not a lot less, but still less) in one of those boxes than you get in the BB.
The point: I'm guessing they see the BB as advertising. They want to get good word of mouth circulating about the product well before release and whet the appetites of the consumer for the full product (it already worked, dinnit?). To get that, I think FFG is willing to suffer a wash on each unit (if not an actual loss) to get it. This means that it'll be a lot less enticing to do this for AoR, and again for F&D. Especially because they'll already have the product out showcasing similar rules: Edge of the Empire.
Really, whats in that box that can't be published over the internet (thereby saving on printing and distribution costs)? The dice and … The character tokens? I guess? When AoR is released, the dice will be widely available since they're the same dice as EotE uses.
So, if the systems are even moderately compatible, the EotE game basically can become a BB for AoR. All FFG needs to do in a year or so is release a short PDF with baby AoR rules and a short adventure that showcase the cool new mechanics AoR has a-comin. And thats a lot easier to do than produce a whole new boxed set.
3) Aside from the dice, after we run the beginner's box will it essentially just sit there gathering dust after I get the core book, and what exists now to keep the game rolling past the box/long arm of the hutt?
4) If I download the two characters they added with long arm… would it be fine to run those two adventures with 6 players?
3) I don't own the BB, but if you don't have the Beta book, I'm guessing the answers are "yes" and "Nothing beyond your own creativity". There's nothing wrong with making your own rules for advancement so you can keep playing with the same core mechanic (narrative dice). Which is cool, but probably not what you're looking for. Maker willing, though, maybe we'll get some adventure modules (official or not) published in the interim or just after release.
4) Don't own it, so I couldn't tell ya. But from my experience with the beta system, I think what Yoshiyahu and Mouthymerc said above sounds really reasonable.
Anyway, I hope that helps. Everything up there really is just my opinion, unless I cited something that said otherwise.
PS Sorry about the $h!tty editing, don't know what happened.