I would suggest using these:
(A) They are listening to the music on the radio.
(b) He is cooking the pasta.
(c) He is admiring his face in the mirror.
(e) He put the goods on the trolly.
He transported/moved the goods with/on a trolly.
(f) He is pushing his baby in a pram.
(g) My mother prepares / cooks / makes meals for us.
I wasn't sure what you were trying to say in sentence (d).