Hi everybody!

So I recently picked up my first rotary and it is a cool little car. It does have a few little quirks I was hoping someone could help out with.

First off it has a slight stutter at idle and at cruising speeds, I was thinking it was a vacuum leak or a its out of time? I dunno just guessing haha.

Second is it has an odd buzzer that goes off when I start it, kinda comes from behind the left side of the dash.

Third is the ''add coolant'' light is always on even thought the coolant level is fine. Sometimes when I hit the brakes the light next to it also faintly lights up. Was thinking a short or something?

Lastly, and most importantly, I have no power going to the headlights. They pop up fine but don't light up like the rest of the lights. I have done quite a bit of forum research in the past few days on this subject but haven't found much in the way of help. A lot of could be's but haven't found anyone with this specific problem.
If I can't figure it out soon I plan on just removing the sealed beams and replacing them with some round LED lights and wiring them to their own switch in the cab, it would be much brighter and I could have them installed in no time.

Sorry for the book haha but thanks for any help you guys can provide