1. He must have bought the bike.
2. He would have bought the bike.
3. He could have bought the bike.
4. He may have bought the bike.
5. He might have bought the bike.
* 6. He will have bought the bike.
* 7. He can have bought the bike.
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Do you mean #6 and #7 are ungrammatical?
What about the others? Do they all mean possibility or guessing? Can #2 mean possibility or guessing?
#s 1 - 5 are all possibilities or guesses, yes.
I don't think #7 is correct, nor do I think it can be fixed. It just doesn't make much sense.
#6 will make sense if you give it context:
He will have bought the bike by this time next week.