Something I've required for most of my Star Wars games (except the very early WEG ones) was that if a player wants their character to become Force-sensitive after character creation, they need to provide justification for doing so; namely, what event happened to trigger this character suddenly becoming aware of the Force? If a suitable justification can't be provided by the player beyond "because I want access to the cool powers" then I disallow them becoming Force-sensitive.
As for learning new powers, under Saga Edition my rule-of-thumb was that the powers in the core rulebook were 'standard' powers that could be learned without any sort of instruction, even allegedly 'secret' powers like Force Lightning (which the movies treats more as an advanced manifestation of the dark side) and Sever Force (light side ability to dampen/cut a foe's ability to use the Force).
For this system, I'd treat is as much the same, that a Force-sensitive PC can learn a new base power without an instructor, but there are a couple caveats. First of these is would be that only one new power learned in between sessions; just because you've got 30 XP sitting in your pocket doesn't mean your self-taught Exile who only had Sense can suddenly learn basic telekinesis (Move), boost their sensory perceptions (Sense), and see the future (Foresee). Second is would be that you can only purchase a single upgrade per power between sessions, reflecting the "slow & steady" path of self-taught abilities; so an Emergent with just the Enhance basic power could either purchase the Resilience Control Upgrade or the Coordination Control Upgrade after a session, but not both. Of course, if the PC has access to a means of instruction, be it an experienced Force user, a Jedi/Sith holocron, or even training manuals discussing particularly Force abilities, then those restrictions are waived as the PC is benefiting from the experience and knowledge of someone that already knows this stuff.
For the campaign that I'm playing a Force user in, the GM hasn't really set any restrictions on what I could or could not purchase with my XP. But I opted to adhere to those two restrictions I listed for my character, to reflect that for sometime, he was slowing coming to understand the nature of the Force and what it could do. Granted, when that same character got about a week of in-game time to study a Jedi Holocron, those restrictions went right out the window (particularly as he'd just taken the Force Rating talent to bring his Force Rating up to 2). Of course, now that I don't have the holocron anymore (had relinquished it as part of an earlier agreement with an NPC sponsor; even worked it into part of his character growth into becoming an actual Jedi instead of a Force user of growing capability), I'm right back to those two self-imposed restrictions as noted above.