No, the URL is the web page address. The QR code is that black and white matrix at the bottom right of my card. You can google it so you know what I mean, @Julia1050 , and how people use it. There are easy-to-use and free-of charge QR code generators out there. Just google that, too.
I'm not good with tips for visibility on the Airbnb site. As you say, everyone wants to be at the top. You are new, so for a little while you will get an automatic boost in the rankings. Filters can help. They are not perfect, but they seem to be getting better all the time.
Do stay on top of your calendar so you don't get booked on a day you cannot host, and do tweak your description and rules as necessary, as you learn from guests what they see and perceive and want. That is important just in general, but I have heard it keeps a listing "fresh" so it doesn't fall to the bottom.
Hope that helps a little!