I'm not sure about the meaning in this case. What was the context? The verb "cap" sometimes means "to provide a conclusion to a situation or story". It could also be the short form for "capitalization". Do any of these meanings make sense?

"Draw a blank" is an idiom that means "to get no response or result". For example: "I asked her this question, but I just drew a blank" (= I got no response).

"Draw a blank" could also mean "to fail to remember something". For example: "I was asked to enter my PIN, but I drew a blank". The expression is somewhat similar to the Portuguese "dar um branco".

Both meanings seem possible. What do you think?

In British English, "hard lines" means "bad luck". Did you hear this from a British person?

It just means "you've improved a lot". It conveys the idea that there is no end to your improvement. Sounds like a compliment to me!