1. Yes, that happens frequently. For this reason, cards like Chaos Warp are quite staple-worthy and often superior to cards which destroy or exile.
2. Your commander should always be in same type and color sleeve as the rest of the deck in preparation for such an eventuality. Similarly, if some cards are double-sleeved, all should be, and only having an oversized commander card without a regular sized copy is also insufficient.
3. No, because it's exiled face down, so you never get to know what it was in order to potentially apply the replacement effect which means you're out of luck until the card changes zones.