No. "back to sleep" is designed to help lower the chances of sudden infant death syndrome (sids) or crib death. Babies who can't roll over are at a much greater risk of sids if they sleep (or nap) on their tummies or sides. So, until they can roll over well, put them "back to sleep.".
No. It is not advised.
No. No. Babies should be put down to sleep on their backs. Once they're old enough to roll to heir tummy themselves, that's fine. But always put them down on their backs. Babies who usually sleep on their backs but are then put down on their tummy to sleep seem to be at an especially high risk of sids. Do not do that.