All I do is cry vs. All I do is crying

English as a Second Language English Vocabulary, Grammar and Idioms
1

What’s the difference between these 2 sentences:

All I do is cry.
All I do is crying.

Why can the bare infinitive be used?

2

The second one is wrong. The bare infinitive parallels ‘do’ better, I guess. These are correct:

All I do is cry.
All I’m doing is crying.

3

Is there a chance that the infinitive can be used?

e.g. All I do is to cry.

4

No chance in my book.