Would I be able to see improvement just by doing ten pushups a day?

Yes. That's called progressive overload. Each week you try to do a little more. It keeps challenging your muscles to get them to grow and get stronger. I highly encourage you to incorporate some free weight exercises though for better resistance.

Of course. There is a 100 Push ups app that is rather fun.

Imagine how many push-ups do ya gotta do by Christmas? Super human.

Yup. That will strengthen your muscles. You'll see in just a couple weeks how much easier those 10 push ups are.

yes but keep in mind, pushups are more aerobic than anything. Get some free weights and work with those.

I wish I had an appropriate answer sorry

Ummm. Maybe.