Tree roots in auto fill pool reservoir and new owner questions

Welcome to TFP.
Several points is provided to you for consideration:
1) Can you remove the roots from the autofill and maybe put some sealant to prevent them from coming back? The autofill is just like a float in your toilet so it is easy to repair. Furthermore, if you have to remove it, you just have to add water manually. Many pool owners don't have a autofill. You just don't want it to get stuck in the fill position where it causes water to rise and then you are draining water at the same time you are adding it - sort of what happens in a running toilet.
2) Not sure how it works in CA but sometimes when buying a home, the seller buys a 1 year home warranty for appliances in the house. You can get the seller to include pool equipment as well. If that is part of the sales contract in CA then use that home warranty to repair the autofill or whatever else is not functioning.
3) It is the plaster that waterproofs the pool. So as long as it is holding water you are good. It may not look good due to poor maintenance but it will be cosmetic. Look for chips in the plaster or soft areas - that is where the problems will be (or start) that tells you time to re-plaster.
4) Following the TFP methodology can get your water chemistry right and have a clear and properly sanitized pool to swim in.
5) Create Your Signature to help us understand what your current setup is for your pool and post some pictures of the equipment if you need help to understand what is what.
6) Read Pool Care Basics Archives - Trouble Free Pool | Trouble Free Pool - this will provide you sufficient info to start taking charge of your pool
Good Luck.