Are the potions that I can make from this college permanent, or do the effects only last a short time?
They have temporary effects. I'm not sure, but I think that the higher your Tech Aptitude is, the longer they will last. They do last for a while though and they're easy to make so it's not likely that you'll face a shortage.
Even with high MA it lasts through big dangeons. I used it on Raven in places like the Dredge and the Bangellian Deeps, and it lasted long enough for me to finish them.