Does purely changing your level to a given number actually impact the kinds of monster you face? E.g., say I am actually lvl 20, but use setlevel to change it to 13.... Will this impact on what monsters I see, as well as the hp amount they will have?

It will. After I set my character's level to 100, All I can see is bandits in glass armor, angry goblin warlords, Minotaurs, and other high level creatures.

It might not look like it in places you've been recently, but those areas will update with your character's level after the respawning interval goes by (73 game hours).

I'm quite the fan of 'capping' my characters' level. I select several major skills to never use to accomplish this. I suppose never sleeping after you hit your desired level could work (but not for me from an RP perspective). I imagine one could also cap one's level by using the set level command. Say my desired level cap is 30: Every time I level up to 31, I suppose I could simply use that command to put it back to 30. I guess that could be an alternative to restricting the use of major skills.