I'm having a question, I would like to ask you.

When should we add "-ing" after a verb?

For example:
"I saw the ship's guns
, catching the light of the moon."
"I saw the ship's guns
which caught the light of the moon."

Another question is:
"I expected him loving me"
" I expected him to love me"
"I expected to love him"
"I expected loving him"