I know the thread is about students from England, Wales and NI going to university in Scotland after independence, but there are some interesting questions about what would happen to Scottish students who wanted to study in the UK.
If Scotland becomes an independent country and isn't in the EU, surely they would be allowed into the European Economic Area or something like that so that their students would be treated as equivalent to the EU for fee purposes? I believe this is what happens with Swiss and Norwegian nationals so they don't get treated as overseas students. It makes an enormous difference to the fees.
Also, would Scottish migrants to the UK be allowed to work or would they be subject to immigration controls? Common sense suggests they would have to be treated as a special case unless there are border guards posted all along the frontier. I don't know whether UK immigration rules before both Ireland and the UK were in the EU made exemptions for Irish nationals, given how easy it is to move been NI and the Republic, but I assume so. It would have to be the same as that, surely?
As for the point about English students not being able to get jobs in Scotland because Scotland isn't in the EU, I don't follow that. Surely the problem is the other way round unless exemptions are made, as I said above? Scotland would make its own immigration rules without reference to anyone else, although given the fluid border with England, I imagine the UK government would apply considerable pressure to make sure there were some controls.