Learn English – Does “I be” mean both “am” and “was”

Yes, all of those are fine. The nice thing about the present perfect is that while it might refer to the past, it behaves grammatically like the simple present.

Both of the interpretations you suggest are potentially correct, and are in fact used in every day speech. However, the second meaning (he did not do it in spite of being capable of doing it) is likely to be the intended meaning only if it is accompanied by additional information about why he didn't do it. For example, He might have done it, had he not been so busy, or He might have done it, but he didn't have enough money. Both of these sentences mean that he did NOT do it, a condition prevented or discouraged him from doing it, and if that condition were different it is likely he would have done it.

When used outside the context of a preventative condition, however, he might have done it is almost always intended to say there is a likelihood he did in fact do it.