Hey @Viktor Korokhov
You can suppress alerts at a given schedule, per Alert processing rules for Azure Monitor alerts - Azure Monitor | Microsoft Learn. But I've reached out to the product group and suppressing as the "last weekend of the month" isn't supported. You're confined the alert scheduling available in the Alert Scheduling.
Regarding
b. if I set scope Management + filter "alert rule name", I can save it in Management subscription, but it doesn't suppress notifications of rule that is placed in Managament subscription for resources in Lab subscription.
It would be helpful if you could provide a screenshot illustrating what you're doing. You can create an alert rule scoped to a subscription you have access to, but I'm not following what you're saying.
EDIT 16 Oct 2023 I've received word from the product group that cross subscription alert processing rules is currently not supported.