Fridge control with 308

I have a fridge that doesn’t hold set temperature,it fluctuates like a roller coaster,I changed temperature probe but still fluctuates.

Can I hold it in range with Inkbird 308,I use it as beer fridge but also planned to use it to cold crash and as fermenting chamber..

Seems the compressor works as goes from 10C to -4C..If I turn it off it cools then goes up and down over hours,I have a WiFi thermometer and shows grapg like a roller coaster.

What Id like is

1 Have it at 3C to say 6C

2 If cold crash -1C to 3C

3 If fermenting(use a heater in fridge) Lager say 6C to 11C..

If beer 18C to 20C

Sorry for the long post.