Engine shuts off when cold and stay running when engine is at normal temperatures

Been having issues with it for the past year and no luck finding the problem.

1. It drains the battery if left sitting without moving it for a couple days.

Replaced a couple batteries but the problem persisted.

The alternator has been tested a l few times, it’s good according to the technician.

2. At first it wasn’t running, looking through forums found some people having issues and some found the fuse box to be the problem.
Before that the coils and spark plugs were replaced.
Other mechanic shop told me that the timing chains needed to be replaced.
Due to not having the funds decided to keep checking on my own.
Checked the fuse box and indeed the box screws were loose and the harness connectors were not making a good connection.
After that the car run good for a few months.
Now the car runs the it just shuts off it won’t stay running, the tachometer would just bounce up and down, surging like.

Replaced the PCV valve, temperature sensor, and throttle body sensor, still same problem.

But if step on the gas at around 3,000 RPMs for about 5 minutes to get the engine warm it will stay running but if I drive the car around the engine will stall while driving.
I don’t know what else to check any advice will be appreciated.
Thanks