To make my brain work or working?

In regard to the first set, they're both correct. In regard to the second, the first one is incorrect.

1) Do you feel my heart beating?
or
2) Do you feel my heart beat?

Both OK.
Do you feel [noun] [verb-ing]
Do you feel [noun] [verb]

Do you see my kite flying?
Do you see my kite fly?

Can you hear my sister singing?
Can you hear my sister sing?

However there is also a noun, "heartbeat". You can say "Can you feel my heartbeat?"

Thank you for your help.
Have a good day.
Serge

Thank you for your help and for your examples.
Have a good day.
Serge