Does Credit Karma (or others) share what CCs you have with any agencies or banks?

I am going through Credit Karma's process of telling it which credit cards I have so that it can recommend others and which are best to use for what things.

It currently can't tell what cards I have with which banks, and doesn't have all my credit cards. For example, it doesn't have my business credit cards or charge cards, and even some cards are missing.

First question: if tell Credit Karma about cards I have like AmEx Business Gold, that it doesn't currently know about, will it report these cards to other CC companies like chase or others?

Second question: I've heard about CK competitors like NerdWallet, CreditSesame, Mint, and Nav. Which do people generally prefer?

Thank you!