The 2 years mentioned is the period from 1 Jan 2021 (when UK licences were first technically able to be issued) to 31 Dec 2022 at which time the UK CAA will no longer accept EASA certficates.
This page makes it pretty clear that any UK licences relying on EASA pass certificates, which includes EASA exam passes dating before exit day, must be applied for before 31 Dec 2022. Relating to your first question "
does this mean that exams taken before the 31/12/20 is exempted in order to acquire the UK license?", there is a process whereby any EASA passes before that date can be credited by the UK and, if they are not all already passed, you can continue your exam series with the UK CAA. It does say somewhere that this process is for people who previously had the UK as their SOLI and are 'returning' but I don't know how strictly that is applied.