I would not get rentals because I think it could be quite an adjustment going from your own skates to those and then back. I once tried to go back to my old skates after skating in new ones for just a day or two, and it was really bizarre. Plus you might try something that requires an edge, find you don't have one, and fall, and those are the worst falls.
All of my friends know I skate, though they don't all know what I can do. I think some think I just go and do laps. I think if I were you, I would mention to my friend that I've been taking lessons, but don't show off or do anything besides laps unless she asks. Why pretend you don't know how to skate? It's not arrogant to admit that you started something new and are working hard at becoming better, and your friend will probably think it's cool.
I had a boyfriend once who told me I couldn't be on his adult soccer team because I wasn't good enough. This was a casual, no tryouts required, let's just have fun kind of team. Now that's arrogant!