1. All are fine, but the last one is a bit odd. I would not use it.
2. He forgot that he had closed the door. He forgot that the door had been closed. He forgot he had closed the door.
I agree that you should go home early this evening. ("agree with you to go" is not a normal combination of words for this context)
3. You deserve to have a good score in this work. I hope to go on holiday to Greece this summer. Carl offered to help me. He offered me a helping hand. <~~All are OK.
My mother promised to go to the doctor.
My mother promised me she would go to the doctor.
She invited me to her birthday party. Can I invite you to have dinner with me this evening? <~~All are OK.
The last sentence would be better like this: Would you have dinner with me?
4. Can I propose having dinner Ö?
Iím resisting the enemy's attack.
He resents having to do this exercise. I have been told to go directly home. <~~All are OK.
5)I warned you not to trust him.
I talked you out (??)<~~I don't know what you mean to say here.
Parking is not permitted here. <~~OK
Parking is not allowed here.
You canít stop me from doing what I want.
6) He needs to go to the dentist.
He has an appointment with the dentist.
He has a dentist's appointment.
He needs to make an appointment with the dentist. <~~All are OK.
7) take/write an exam (do is a mistake?)
<~~The first two are right; "do" is not.
make a decision (take a decision is a mistake? <~~"make" is right; "take" is not.
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