I would like you to clarify a few point to me (Can you say that?)

Which is the best verb to be used with "doubt"?

1) The teacher made me repeat the exercise. Passive: I was made to repeat the exercise (by the teacher : can it be omitted?)
2) He requested me to go for a motorbile ride (better: He invited me to go..)
3) He excused for breaking the vase.
He excused because he broke the vase (is it possible?)
He apologized for breaking...
4) "If I were you, I'd leave tomorrow morning", he said.
He said that if he were me, he'd leave the following day.
5) "Come in and shut the door." He ordered/commanded/asked to come in and shut the door. (Can "us"/"me" be omitted or is it a mistake to omit them?)
6)He forgot to remove he coffee pot from the gas and the coffee boiled over.
(Do you say "put the coffee pot on the gas and turn on the gas??")

I would like you to clarify a few points for me.

Which is the best verb to be used with "doubt"?
If "doubt" is to be used as a verb, too, there are lots of possibilities. One example is this: I doubt he would be able to complete that assignment. (subjunctive mood for "would be."

1) The teacher made me repeat the exercise. Passive: I was made to repeat the exercise by the teacher. It's clearer if you state who did the action in that passive verb, yes.

2) He requested that I go for a motorbike ride (better: He invited me to go..)<~~yes, that's better

3) He excused for breaking the vase.
He excused because he broke the vase (is it possible?) No, sorry. These are correct: He was excused for breaking the vase. OR He excused his sister for breaking the vase.

He apologized for breaking... <~~OK

4) "If I were you, I'd leave tomorrow morning", he said.
He said that if he were me, he'd leave the following day.
OK, if you put a comma after "that" to match the comma after "me"!

5) "Come in and shut the door." He ordered/commanded/asked me/us to come in and shut the door. (Can "us"/"me" be omitted or is it a mistake to omit them?)
It's an error to omit them.

6)He forgot to remove the coffee pot from the stovetop and the coffee boiled over.
(Do you say "put the coffee pot on the stovetop and turn on the gas??")
alternates for "stovetop" are these: stove, range, burner