No. You’re not being paranoid. Fathers do not kiss teenaged daughters on the lips or touch them on the butt. Responsible fathers don’t invite their daughters to be sexual objects (metal girl? Really?). It’s his job to give her a safe relationship. It’s also his job to show her how to be in a relationship by being in relationship with you, not her. She should be watching the two of you sit close on the couch. You shouldn’t be watching them! Please.
Draw clear, solid boundaries. Do not let her go to his place without you. Put an immediate stop to the hugging and kissing. Your daughter may resent it now but when she grows up and matures, she’ll thank you for keeping her safe. And please think again about whether this is the guy for you. Why would you want to be with a man who has so little respect for you and your child?
I wish you well.