How do you gain a higher force rating? I have seen one talent (always way at the bottom of the tree) and that you get one each time you buy a specialization (right?). But is there any other way?

If you start in an F&D spec, you start with FR 1. Other than that, you can only increase FR by taking Force Rating talents. If you're an EotE or AoR character, you get FR 1 when you buy into the Exile or Emergent tree, and can only increase it by taking Force Rating talents afterwards.

I hope this helps.

When you begin with a career from Force and Destiny, you begin with a Force rating of 1. This information can be found in the first paragraph of each career description in the book, where the six career skills are listed. The Force Rating talent is the only means to increase your Force rating permanently afterwards. Keep in mind that this does not give you a Force rating of 1 if you do not already have it. Further, purchasing a specialization from one of the six Force and Destiny careers does not grant a Force rating, either. If you start as a Bounty Hunter, to get a Force rating of 1, you have to purchase the Force-Sensitive Exile or Emergent specializations from EotE/AoR, which grant a Force rating of 1, before you can reap the Force talents in any of the F&D specializations.

How do you gain a higher force rating? I have seen one talent (always way at the bottom of the tree)

Not always at the bottom, but this is the only way to increase your FR past 1.

and that you get one each time you buy a specialization (right?).

Not right.

If you have an FR of 0 and you buy either the Exile or Emergent universal spec they give you an FR of 1, but that's all they do, and it's a [you gain an FR of 1 if you didn't have it already] not [you get +1 to your FR]

All the Specs in FaD have the FR of 1 attached to the Career, not the spec, so you can't make a Engineer:Mechanic force sensitive by buying into Artisan, you've got to get either Exile or Emergent.

FR is a pretty powerful thing, so there's a reason it's hard to get.