Instead of punching horizontally some pad/sack/dummy on a wall or hanging from the ceiling, could we place a (properly cushioned) pad on the floor and train punching it (the position would be like a one-hand push up)?
Can you...sure you can, but you defeat the body mechanics and technique which is the main goal of the training. Punching a standard bag or wall pad allows you to position your body and punch with pivoting as well as proper technique to train your body to punch properly as well as increase your skill and power. On the ground like you mention you eliminate your lower body and pivoting for the punching. You also eliminate your upper body except for 1 arm because you have to hold yourself up with the other hand.
If your limited on means it would be better to hang a pad by a string and practice proper technique even if you can't see the power due to little resistance than it would be to mess up the body mechanics and practice bad form.
Yes, you can. Indeed, there are human-shaped targets that the MMA guys at my gym often sit on top of while working on their downward punches, or even wrapping themselves around it from underneath and hitting into the kidney area. While mutt's right that a standing punch lets you engage more muscles and get more power, that's no reason not to practice punching from other positions where it may still be your best or only option. The more versatility you have using your techniques, the better. It's not to "practice bad form", but to understand how the form should best be varied with your and your opponent's position. That said, if you don't have a good standing punch, it may be a good idea to work on that first - it will give you a better idea of what bio-mechanical elements you should at least be trying to utilise from a more prone position. And a "one handed pushup" position doesn't sound like something coming about often during ground fighting anyway....
Can you practice punching a target on the floor? Yes, you can.
Yes, if you want to get good at punching an opponent on the ground (say, who you have just thrown).
It doesn't seem like it would be a good substitute for practicing a punch for situations where both you and your opponent are upright. The body mechanics are quite different.
Since your question included the phrase "instead of," I would answer that it would not be wise for this to be your primary punching practice. Always practice in a way that most closely resembles the circumstances in which you expect to deploy a technique.