Treat methylation as binary or continuous signal when detecting DMR?

Methylation level is usually measured as continuous value (M-value from 450K). However, DNA methylation is binary outcome in nature (methylated or not), and it is relatively easy to make the conversion since methylation is bimodal around 0.2 and 0.8.

1: When we are to detect DMR (region) or DMS (site), do we want treat it as continous value and use test like T-test? Or do we want treat it as binary value and use proportion test? My intuition is to use binary value when measuring DMS and to use continous value when measuring DMR (for instance taking averge level across region)

2: I read several threads saying Fisher exact test is inappropriate for DMR detection due to not accounting biological variance. In that case, I guess T-test or Possion test is inappropriate to use when treating them as continuous value, right? May be using negative bionomial distribution?