Some questions about some problems

Now one day, I came from work and started my car. It just didn't start. Even the starter wasn't turning. I wondered, what could cause this. Day before it was ok. So I'm thinking to try a new battery (the old one is about 8 years old I think). What is the correct size for the 1997 ATM? I'm thinking about the AMP-s and Ah.

Next one is that sometimes my car wants to stall and sometimes it does when I break. I am thinking about vacuum leakage etc, but what should I look first?

Has somebody got a electric schema for back lights? My country is quite hostile for red turning lights and so the Escorts rear turning lights we're fitted into backing light. Now when I saw what shitty work they had done, I wanted to do everything again and correctly.

Also the solenoid, that is inside next to shifting plate. It's blue wire has been cut and connected to brake switch and from there to back lights. Whats the deal with the blue wire? What does it do?

Thanks.