Separation/Terminator due to the zero tolerance policy - would I get payed for the two month or the days I worked?

I have been given two options i.e. Separation/Terminator due to the zero tolerance policy, and I did resign officially, but I don't need to serve the notice this is what my designated HR conveyed, usually, we have to serve two months, the question would I get payed for the two month or the days I worked but she also said she will do some changes in the backend (Changing the relieving date)

This would depend on the company policy in this regard. You will have to wait for the HR decision on your relieving date and it can be expected that they will pay you till then.