Can I obtain a right of permanent residence even after 31 December 2020?

Yes, that is possible. You are required to have lived in Germany for five years, with interruptions of up to six months, or up to 12 months in exceptional cases (more). Periods before and after 31 December 2020 are added together. You automatically have the right upon fulfilling the conditions without the need for an authority to take action. If you wish, this can also be certified on a residence document.