Do I have to do anything special to remove, say, Intense Training perk, if the player took all ten levels of it, or will a single player.removeperk work?

It maybe best to setup a test effect with a magazine. Write up a simple script that does the player.removeperk perkname and save it as an effect script. Tie that into the magazine through a base effect that selects the script then test it out in a test plugin. If it only removes 1 rank of the perk then you'll need several successive removeperks. However i'm thinking you won't need that many because even though the perk is ranked it is still a base perk that will be removed.