Besides rank lowering equipment is there any restrictions on items that can be used when running IL's? And is there any sort of category in which you can use rank lowering equipment? I'm sorry if this has already been answered somewhere and I missed it while I skimmed looking for an answer in the stickied threads.

Any% is what you're looking for when wanting to use rank lowering items. And as far as I know there's no other restrictions.

Any% = What ever you want beside Gray Fox / Raiden as they are 30% & 50% sprint speed faster. after that you have Any% Raiden(& Gray fox but who would use a slower version of Raider ?) wich allow the same things as Any% but with raiden outfit.

That is as simple of that ^^

Hope your question is answer feel free to ask in this post if you have any other question.