Hmm... good catch. It start to become clear now... CR 619575 is not fixed and it looks like it may not be fixed soon.
The rationale is that compatibility mode aims to have the same behaviour as ASE 12.5.4 and in doing so it follows a different internal code path than non-compatibility mode. Updating the counters that are exposed via MDA was not happening in 12.5.4 either and therefore is not being done under compatibility mode either.
I know it's inconvenient, but that's the reason why.
(and the bug is marked as closed which is why I didn't find it as I looked for open bugs the other day)
You could always open a techsupport case and request this bug to be fixed after all, but I don't give you a high chance of success.
On your question #2: the MDA tables take their data from internal memory structures that are maintained inside ASE. When you query an MDA table, whathappens is that the data from these memory structures is presented as if they were rows in a table (in reality, the MDA tables aren't real tables of course).
Many of these counters are maintained irrespective of 'enable monitoring'. However, there are also counters that can impact overall ASE performance and for this reason there are various config parameters that enable/disable all or part of the MDA functionality.