офф. грамматика to+Verb or V+ing? gen.

[Новичок8]

I've been studying English for a long time now, but still have confused spots to learn more about.
Could you please advise me on the following please?

Person A: Has Jill arrived yet?
Person B: Yes, I think, I heard her....come or coming?

And one more:
- Can Tom play the piano?
- I've never heard him....play or playing?

And finally:
- Did the doorbell ring?
- I'm not sure. I didn't hear it...ring or ringing?

What is difference in meaning?
I need to know the subtliest details. :)

Thanks

[silly.wizard]

subtlest

[miss_sunshine]

see grammar textbooks by Raymond Murphy or Betty Azar

[Francis Fanon]

Example 1: Either is possible, no difference in meaning. (запятая не нужна после think)
Example 2: "play" is more normal. If you said "playing" it would imply that you often saw Tom doing various activities, just not playing the piano.
Example 3: "ringing" implies that the doorbell rings for a long time when someone rings it