That sounds brill, as you say though, there are many ways of doing something, so personally, I wouldn't practise something she hasn't specificly shown you how she want it done. I think like you say, practising her way of polishing, or for example her way of performing a manicure and nail prep is a great start, you know how to do it your way, now you just need to train yur brain to do it her way.
Anthing else, I think I would just be annoyed I spent time trying to learn how to do something myself, only to find out my tutor teaches me to do it in a different way, or with different products etc, it's so much harder to re-learn something.
Also, the last thing you want to do is spend a lot of money on products that are the wrong ones, or you'll never use again. Been there done that, and my bank balance wasn't happy.
Play with the products you have, maybe practise some nail art with your gel polishes, like you said, she's keen for you to pick that up so you can always get a head start with that!
