Forgot Apple ID password and Recovery key

Hi!

As the title says, I don't remember my Apple ID password and I don't have my recovery key. I have two-step verification turned on, so I can't access my account. I am still able to use my iPhone, but I want to buy another one and to transfer everything I have on the newer one. How will I be able to do that? Have I lost my Apple account forever? I have Find my iPhone turned on and I can't even turn it off without logging in...

Please help! Thank you!

Bogdan