Hello does thermal paste just cool the heater quicker or its needed?
I was cleanening the heater and acidentaly removed a lot of paste with it.
Or like will it survive when i will use it without the paste for like a week?
Yes, thermal paste is necessary to better/faster transfer heat from heatbreak to cooler. Without it, temperature in upper part of heatbreak (coldend) will be too high and you can expect clogs & jams. Because of higher temperatures in coldend, PTFE tube inside will shrink quite fast -especially if you use stock heatbreak.
That is, if you use it without thermal paste, you won't damage printer.. but after a while (one hour, two hours?) it just won't work as expected and you'll be forced to clean the mess inside heatbreak -at least that's my prediction.
Btw. If you only print PLA, then thermal paste for CPU cooling will do the job at least temporary (is much better than nothing).
Noctua Thermal Paste
I use NOCTUA thermal paste for my PC's (Both video cards and CPU's.) It's good for 110 degrees C. IF you have a proper heat break in your mini, even the stock one is fine, it should work. There is a video on youtube where someone measured it with a Bondtech, stock and a clone and the bondtech and the original were much lower than 110C. I can't remember what the clone got to, it was higher though. IF you have to order anyway, just get some copper based stuff that's good for 3D printers.