Hi there!
In my experience, both as student and teacher, foot-tapping was and is absolutely useless. Mr. Bearz shows the key:
You use your brain to keep time (...)
Indeed, when you're playing something that you already know the rhythm, you can tap your foot, shake your head, make noises with your tongue: any of these practices will be just another line that you add to the music. But what happens when you reach a section with a hard rhythm? Your foot stops, or taps out of beat. The same applies for Bach, for instance. A major problem with his music is keeping the same beat in
moto continuo pieces. Someone could think that foot-tapping would help, but again it is pointless: just record yourself and you will notice that the taps of your feet are irregular.
By the way, recording is a great idea for both question: rhythm and tempo. Another very useful tool is using the metronome to figure out where you're getting out of beat.
Again, all the music is in your brain. It controls your hands, and thus your playing and expression.
Best wishes!