Can one say:
1-I heard that he shouted.
a-I heard him shout.
I do say: "I saw that he walked out of the room." I think that structure works with "see" but does it work with "hear"?
I never use "1" in this sense. If I say "1" it would mean "I was told that he shouted."
We can hear somebody/something doing something:: "Jenny could hear them arguing outside" or we can
hear somebody do something "She heard Tom go upstairs".
If you say hear that as in " I'm so sorry to hear (that) he died" it means you've been told about something or you've found out information.