Q: If my Keepers are Invisible, they’re immune to cards like Exchange Keepers, or Mix It All Up. Does that mean I can’t play those cards myself?

A: While your Invisible Keepers are immune from such Actions from other people, you are allowed to play them yourself. After all, presumably YOU know where the item you’re exchanging is, even though it’s Invisible. By contrast, other players don’t even know your Keepers are there to be Exchanged with.