1) By the rules, once you select a career then your character is stuck with it. However, your GM might allow you to rebuild your character using a different career if you really feel that your initial choice simply isn't working out.
2) Yes, as detailed on Page 93 of the core rulebook, namely being 10 x number of existing specializations you have, with an extra 10 point cost if the specialization isn't attached to your career (universal specializations are exempt from this extra 10pt cost).
3) Incorrect. Once you acquire a specialization, it's yours to keep. Back in the EotE Beta there was a rule that a PC could only have three specializations at most, but that got dropped pretty early. Now, you can have as many specializations as you can purchase, and you get to keep any talents you've purchased.
4) Yes, you can take any specialization you want, so long as you have the XP to pay for it. Your GM might require to explain how your character picked up the basic know-how for that specialization, particularly for odd cases like a Bounty Hunter/Assassin suddenly grabbing the Slicer specialization, or a Colonist/Doctor grabbing the Fringer specialization, but going purely by the rules there's no requirement other than paying the XP cost as noted above. The in-game justification may be especially relevant if you want to grab the Force Exile universal specialization, particularly if nothing about your character's background ever suggested they were Force-sensitive.