Once you redshirt, the "redshirt" moniker stays with you no matter what class you're in. For example, AJ redshirted in 2009 and was a redshirt freshman in 2010. He was a redshirt senior in 2013. In your example above, if Jalen never redshirts and leaves early, he will be a Junior (specifically a true junior).
Exactly - Jalen is a "true" freshman starter because he "truly" is a freshman, both in terms of academics and football eligibility used. Barnett would have been a redshirt freshman this year if he had stayed because he was redshirted in his first year at Alabama - he would have been a sophomore academically, but only a freshman with respect his football eligibility since it would be his first year playing.
In football, think in terms of playing eligibility. You are a freshman (true or redshirt) if you are
using your first year of football eligibility that season. You are a sophomore (true or redshirt) if you are
using your second year of eligibility. Etc. Most of these players are in school for more than 2 semesters anyway with summer classes, so tracking them based on academic calendars is almost impossible. Watson graduated in 2.5 years at Clemson, for instance (he just finished his course work for his degree). This year he was a junior in terms of his football eligibility, but a senior academically.