On the EU-spouse tack - As someone above said, it's taking only a few weeks to get a EU family permit. (I'm pretty sure ours took longer, but I was counting mailing time at both ends in that, and it was in 2016 around the holidays, and I've slept since then, so....). Once you have that you can enter and exit the UK several times, within the validity period of the permit. Assuming the UK is still in the EU during that time. SO if you have to run back to the States for something, you could do that.
https://www.gov.uk/family-permitIf there's a Hard Brexit, the UK is still saying that they are going to honor EU citizens' residency here. So if you're over here by then, you should be ok.
If there's a soft Brexit (or no Brexit), you should be ok over here. With the usual caveats.
If you come in as an EU spouse, you don't need the Tier 4. You will show them your EU residency card and have the right to work and live in the UK on the same terms as a national. You'll still be popped for international tuition and fees, most likely, until you've been here three years, but you would be free to attend. I remember seeing something in the past few days about as long as your sponsor had been in the EU for three years, you could get EU fees even if you had not been here that long yourself. But that might have been a special circumstance situation. Worth checking.
As Sirius points out, though, EU citizen status is somewhat shaky here. The UK can change the law or their policies towards EU citizens at any time once the UK is no longer in the EU. Turn around and turn us all out. Unlikely, but they can do it. Or make our lives so miserable we don't want to stay.
Right now, what they are saying is that for Hard Brexit, if you're here
before we crash out, you can stay. You'll have to file for pre-settled status and then after 5 years file again for "settled" status. (Like a US greencard.) After that point you can apply for citizenship (maybe another year's wait, not sure). If you don't make it over on the family permit before Brexit's cliff, you have to use UK immigration rules, not EU movement rules. MUCH harder.
If we DON'T crash out, and there's an implementation period involved, as long as you get here before the implementation period ends, you can apply for pre-settled status, and then after 5 years for "settled" status. You can then live here indefinitely unless you do something criminal or become a threat to the country. And, of course, they can change that at any time. So until you are a citizen, your rights are less solid.
If they delay Brexit by some major wheeling and dealing (which I don't see the EU agreeing to unless there's some significant chance the UK govmt can get their collective heads out of their collective backsides to actually propose something even reasonably acceptable, or to give them time to hold another referendum), you can still skittle in on EU rules. (So far.)
https://www.gov.uk/settled-status-eu-citizens-families/applying-for-settled-statusSupposing you do the EU family permit. As soon as you get over here, you would normally want to file for an EU family member residence card. (Technically you have three months, but I wouldn't wait.) With Brexit looming, I'm assuming they will still issue them. (But Who Knows?) Otherwise, register for pre-settlement ASAP. Supposedly the system to do that will be "live" by the current Brexit date. Once you have pre-settled status, you should be able to have proof to show your Uni that you are legal to be there and studying.
Good luck!
