I think your suggestions are great. I have a 2 year old and I also try to give him activities that mimic what my older kids are doing. If they're working on worksheets, I'll give him a coloring page. If they're cutting, I'll give him paper and safety scissors. During instruction time, I'll give him an eraser, dry erase markers and a lap sized dry erase board. I think that's his favorite.
I do a lot of hands on work with my kindergartener, so while I'm teaching her I'll let him play with the manipulatives we're using - counting bears, lacing cards, flashcards, alphabet magnets - stuff like that. I think he feels like he's "doing school" too.
I do have a few special toys set aside that I'll pull out during school time and I think it helps to rotate those in and out so they feel new.
I used to try to teach my children during naptime, but I prefer teaching everyone in the morning and giving myself some downtime while my toddler is asleep.