01 325i first time owner, problems

To start off by saying hi, new to the forum. My name is Brandon, I am a new and first time owner of a BMW. The 01 325i to be exact, manual trans. Ok for starters, my water pump was replaced and all before I got the car. The heat isn't working well, except when I'm on the throttle. Secondly my dash warning lights are on, by false I'm sure. The engine service, coolant, brake even when I put the e brake down, sometimes the car light with the little light in front of it, the seat belt when seat belt is clicked in, and I believe one or two more. Car functions really well but I have noticed the break grabs barely sometimes when the brake light first comes on. Once again I'm very new to these, I do want to fix it and am aware that they get expensive. I appreciate everyone's help, hope I can get guided in the right direction.