We're planning on starting a EotE game and I bought the beginner box to start with. When checking the online pregens I noticed that they don't have obligations? The plan is to start with the pregens and then move on to the core game if we like the system, but keeping the characters. Are there instructions how to "expand" the characters when moving to the more complex system?

The Beginner box pregens also seem to have a background but the characters kind of lack personality. By this I mean that there's a background for each character, but they don't really explain how each character's personality and how she acts (cowardly, stupidly brave, noble, etc.etc.). I guess this is up to the players, but since one reason for us to use the pregens is to give fresh ideas to the players who always play the similar kind of characters the lack of "instructions" is bad news. Now there's no written down personality quirks that force the player to make "bad" choices for the characters. Are there these kind of things included in the core box?

While the descriptions don't outright tell you how they'd act, you can sort of infer it. Using the online characters - Sasha was an idealist and the seeing everything go to hell when she joined the Rebels may give her some initial trust issues with anyone they meet - she'll likely always be wary of situations, but she'll still always try to help people she thinks are in need. Mathus is always looking for something to tinker with - whether it's just repairing, modifying, or actually building - and has a strong devotion to people he cares about, and ensuring their safety.

In terms of obligation. Much like Age of Rebellion's beginner game, where it follows the rules for giving a group a base and the bonus in credits that follows, the beginner game for Edge of the Empire is likely set up so that the group fleeing Teemo is sort of earning their obligation. So if you can just give everyone a flat Bounty obligation from Teemo. But if you want to change things up, you can also split it however you like based on each story. Mathus maybe in Obsession with mechanics, or Responsibility to the shop owner. Sasha with Oath to help people in need, or maybe Criminal for her ties to the Rebellion.

The beginner rules are scaled down. This boxed set can be used to start your EotE game, but you will need to make some updates to the characters to make them ready for the full rules.

Things your characters will not have in the Beginner Rules:

1. Specializations (You can kinda guess what they are going for by what skills are picked for the pre-gens)
2. Separate piloting skills for planetary and space.
3. Background titles (pg 36 of the Core Rulebook)(you can figure it out from the characters background stories)
4. Obligations
5. Motivations (once again, the character bios can help figure this out)
6. Beginner game just has a generic 'Knowledge' skill while the Core Rules breaks it down to several categories.
7. Full list of talents for the specializations.
8. The Krayt Fang has different stats than a stock YT-1300.

There are probably other things I'm forgetting as well, but I think I got the big ones.

Like Lathrop said, the story gives you the ship that groups are supposed to start with, and it should give you starting obligation as well with Bounty. You can say 5-10 obligation from that and see if the players want to have a second obligation for their personal story. With 4 players they don't want each player to start with over 10 obligation, so keep that in mind.

I think it has been suggested before that you can have the players rebuild their characters after the Beginner Box adventure (and Long Arm of the Hutt) with the full rules. You can give them the gear/credits they have already accumulated as well as XPs when creating new characters. That works out well because the Beginner Box characters start with gear that would be hard to afford with the regular rules and still have 400 credits left over. This will give them a chance to allocate points to their personal tastes by how they played their character.

Actually the Krayt Fang is a stock YT-1300 with two attachments: a High Ion Thruster and Smuggling Compartments. I easily converted that puppy when they stole it.