1. Don 't hang up. Hold on, please.

2. Don't hang up. Hang on, plese.
(Can we use 'Hang on' instead of "Hold on' in telephone conversation?)

3. He and I made poses like models.
4. He and I made a pose like models.
(Which one is correct? Do we have to use the plural form 'poses' here?)

5. If he runs fast, he will not be late.
6. If he runs quickly, he will not be late.
(Are both the same and grammatical?)

I'd use #1, #3, #5, and #6.

"Hang on" is too informal, in my opinion. Using the "Hold" button on a phone leads to the "Hold on, please" request.

And yes -- in #4, you need plurals since the subject is plural.

1. Yes, you can use "Hang on" instead of "Hold on" in a telephone conversation. Both phrases mean to wait for a moment or to stay on the line.

2. Both "poses" and "pose" are grammatically correct, but the correct choice depends on the intended meaning.
- "He and I made poses like models" suggests that you and the person mentioned were striking a series of different poses, imitating models.
- On the other hand, "He and I made a pose like models" implies that you and the person mentioned struck a single pose together, imitating models.

3. Both "fast" and "quickly" can be used in the sentence "If he runs fast/quickly, he will not be late." Both are grammatically correct and can be used interchangeably to convey the same meaning.