"Rest days" are not legal days off. A legal day off has to include two local nights so if you have a duty that finishes after midnight the remainder of that day becomes a rest day (you will be too knackered to do anything anyway). Similarly, if you have a duty that starts between midnight and 6am (lots of those by the way) then the previous day is a rest day.

Hope that makes sense. Almost all layovers are around 24 hours so there is very little opportunity for days off down route anyway, but the company doesn't count those days towards you legal minimum of 8 days off a month (yet!).

There is no minimum requirement for days off between trips at home unless they are ultra long haul or covered by an annexe to the FOM.

So say that you show at 2am on Monday. Is Sunday counted towards your days off for the month?
I know you have to be off that day, but does it count as one of your days off in a month?
If you had 12 days off in the month, would that be included, or would it actually be 13 days off in that month? (even though it is a rest day)

Just trying to see how much time off you really going to have.

No, legally Sunday could not be a day off as it does not have a local night at each end of it. Therefore it would be a "rest day" but would not count towards your minimum days off that month. In the scenario you describe you would have 12 days off that month.

Take a look at CAP 371
 

Raise or Fold take a look at the UK CAP 371 Document which EK FTLs are based on Select Section B then select Days Off
Link Here