I can't find a way to understand how the HL is working in timeline:

ZVSE

!?HL-1;
!!HE-1:S?y1/?y2;
!!FU&y1=14/y2<2:E; **if he has Fire basic, exit
!!HE-1:S14/3; **set to fire expert so the skill is not offered.

How to restore to fire advanced from now, as I can't see how to post trigger the HL?

Your second option is the best and the easiest to script. But the player will complaint that he invested one level into a expert skill which is not working at expert. So, maybe use HL to automatically advance the skill to expert when he reached advanced. And limit it with BA.