04 micra stalling and battery drain

Hi there

Just bought this 2004 K12 Automatic Micra. I have two major issues with this car.
It sometimes cuts at traffic lights (usually when cold). When starting from cold the car seems to cough up a little and rev goes down as if it's cutting off, which sometimes does. Guy I bought it from said he changed the timing chain on it a few months ago. Engine management lights is on and I have had it plugged in and it's showing cam sensor fault. Previous owner recently cleaned the cam sensor and error went away but then came back.

Also, there's something that's draining the battery. When I lock the car it lets out a long beep even when all doors are closed. Reading some of the posts, people are pointing at boot switch but I haven't noticed any issues with it. It locks and unlocks fine. I have disconnected the boot switch just to check and the beep is still there.

Any idea what that could be and what's draining the battery?

It's pain in the butt when engine cuts off when battery is dead. Jump start works perfectly fine.
Thanks in advance.
 
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