It's okay but nobody would says "two by two", unless referring to Noah's Ark. We always say 'in pairs' or 'in twos'. So while saying 'two by two' would be understood, it would sound odd.

Yes, it is OK to say "two by two". For example, The animals boarded on the boat two by two. You would be saying that the animals boarded the boat in pairs. So yes, you can.