Original Lazer ZX advice please

[schmoov3]

Hello Everyone. This is my first post here as have been away from the hobby for many years. You know normal stuff. house, kids, money, no time etc. Anyway, I have recently been helping my dad sort out his loft and i found my old RC gear. A Tamiya Hornet from the early eighties which isn't in the best of shape, and my Lazer ZX from 1989. This is in very good shape apart from some bodywork damage due to how it was stored. To be honest, the car wasn't used a great deal and was never raced. All original with an old speedmaster silver star ESC. My first thought was to sell it if I'm honest, but when I showed it to my daughter she was very eager to get it going again which would be great for old times sake and I would like to get back into again. No heavy bashing. Just running it on car parks and flat beaches. I have been reading many threads over the last few weeks regarding these cars but there are a few questions I would love some help with if you could please. This forum seems to be full of people with vast knowledge and always willing to help people when needed so any responses would be gratefully received.
1. Wheels and tyres; From what I have read it seems that people can use the mad rat range as they are a direct fit?
2. Bodyshell; Would the parma tomcat repro be a perfect fit from Kamtec and do they sell the under body?
3. Modern Electronics; I would like to run a brushless setup. Would this be safe to do so? If so what modifications, if any, would I need to do, and what would be your recommendation on the brushless power and lipo setup.
4. Spares; It seems a lot of spares are still readily available but are there any parts which are extremely hard to come by?

Thanks again for your time in reading this.