Can a character with force rating 1 or higher take an Age of Rebellion force power (10 xp)? Or do they need to add the Force Sensitive Emergent specialization first?
Is Force Sensitive Emergent required to take new Force Powers?
provided the GM allows them, they can take any of the force powers from AoR provided they have a Force Rating.
What Logan Ambrose said -- if the beta (and final thereof's lack of changing this) is indicative of the core book, then by RAW Force Rating 1 is the only requirement for any of the powers in both EotE and AoR, and both Force specializations provide that.
What Chortles said. The only pre-req currently listed is Force Rating 1+. So if you're a Force Sensitive Exile, you have a 1+ Force Rating, so you're good to go.
-EF
The final AoR beta update further endorses the idea atop page 7:
Most of the elements in Edge of the Empire , Age of Rebellion , and Force and Destiny can simply be brought into any of the other game lines with the GM’s permission and very little extra work. Species, equipment, adversaries, Force powers, and many other elements of the game all use the same rules systems regardless of which book they came from. Using these elements together is not only allowed, but encouraged (as long as it fits into the GM’s campaign, of course).
Neither the Force chapter nor the GMing chapter mention 'cross-compatibility' as far as the Force goes, the latter only lays out clarifications on Obligation and/or Duty and on the repeated-print specializations, so it's just a matter of the GM OK'ing powers from outside EotE.
Right now the only reason for a Force Sensitive Exile to buy the Emergent specialization is access to the the Emergent's talent tree, meaning new unranked talents, and more ranks in ranked talents... in particular access, to a second instance of Force Rating, as currently the only way to reach Force Rating 3 is to acquire it in both specializations. (I'm not sure if Force Rating and Dedication are " formally " ranked talents since they lack the " Add/remove <boost/setback> per rank of " wording, but in practice they are.)
If you look up their descriptions in the Talents chapter, you'll notice they are listed as ranked.
-EF
Don't know about anyone else, but I think keeping them limited to their respective Specializations helps to flavor the different kinds of force users.