There's no formal definition of MRR. Do you count transactions refunded as fraud after the fact? What about transactions that were partially refunded by your support team? What month do transactions that take more than one day to settle fall in? Of course that needs to be timezone-adjusted as well. What about the case where recurring transactions fall on the 30th and 31st of each month? They'll be processed on the la…
You usually track MRR based on users who are currently paying for your service (summing recurring subscription amounts, as you put it). Whether their payment falls at the end of the month or is delayed a day to the next month doesn't affect MRR. Most subscriptions must be paid before the billing period begins.
Things like cancellations or chargebacks are counted separately and would not affect past MRR calculations. No you never count free trials. Yes, you count people who have a credit or balance assuming they overpaid to get that balance. If it was just given as a comp, then no.
Yes, you count people who are set to expire until they actually expire and don't renew.