He knows his skill vaguely because he's likely older several decades, so how could he imply he knows about it to Harry without revealing his identity?
Of course he needs to be manipulative and lie to Harry, imagine if he would outright say
"I have a vague memory of your, or should I say my skill, so let's see what my past self was all about"
Current Harry is very well aware of the lack of refinement of his skills, this is a huge point about
him until he takes on Molly as an apprentice. This forces him to actually go back to school as you will so he can be a decent teacher for her. It is very unlikely that he would forget this, wizards don't.
Isn't there also a "rule" concerning time travel? Why it is discouraged or forbidden about the consequences of meeting one's self in the past or future? Cowl would know about this and it is unlikely he would deliberately confront his past self.
he didn't know his past self would stop him, what harry did when he stopped it was obviously a choice.. he was probably trying to keep Harry from reading the book to begin with. I just said it was about changing the fate of the book itself, not Cowl learning how to do the dark hallow.
Oh, well for a guy who wasn't interested in learning how to do Darkhallow, Cowl made a pretty good
attempt to pull it off. I guess it makes as much sense as Mavra is really the future Murphy. She made a deal just before the battle with the Titian and now she gets to come back from the future as the undead Mavra to get the book. Actually it makes more sense because future Murphy has incriminating photos of herself to blackmail her past self and Harry if she doesn't get the book. And she actually succeeds.