1. To make a guess today's topic

Question

2. To listen to teacher's explanation
3. To write own reviewing note

(Are the sentences above correct?)

4. To make a guess about today's topic.
5. To listen to Teacher's/the teacher's explanation
6. To write your own reviewing note

(What about these sentences from 4-6?)

Answer 1

These are not complete sentences. They are all infinitive phrases.

Here are sentences using those ideas:

I made a guess at today's topic.
She listened to the teacher's explanation.
You need to write your own review notes.