Advice needed for a first-time catsitter who is a bit nervous around cats

I am currently cat/dogsitting for friend and, whilst I have looked after/been around dogs before, I am at a bit of a loss when it comes to the cat. I genuinely don't know what is normal and what is not, and I am also a bit nervous because I had an asthma attack related to a cat when I was a kid. However, it has been 20 years and I have been around cats before (if not nose-to-nose contact) with no issue -- and I have brought my allergy medication and my inhaler just to be on the super duper safe side.

I am only watching them over night, but I think I just want to make sure that I am doing everything right and that my nervousness/general presence/overcautious distance isn't freaking her out. Any advice anyone can offer would be great.