I don't understand what you mean by "not very specific" but I can tell you that the sentences you have marked "wrong" are indeed wrong. Only an infinitive is possible with a modal/defective auxiliary and dare and need when used grammatically in the same way as the modals. There are two infinitives in English, or, if you count active and passive infinitives separately, there are four.
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Cool BreezeI don't understand what you mean by "not very specific" but I can tell you that the sentences you have marked "wrong" are indeed wrong.
The modal auxiliaries are: can, could; shall, should; will, would; may, might; must and ought. Ought is followed by to, in other words, a full infinitive.
Present infinitive:
Active: He would write it.
Pass
kook jEven talking about the (unreal) past that is not related to the present, we don't say:
If I had helped her more carefully , she would had died peacefully last year. (Wrong)
The kids were very quiet last night. I needn't had worried. (Wrong)
That was very critical mistake, I shouldn't had done it. (Wrong)
Instead we say:
I