Node maintenance for patching muting versus unmanage

If I select mute alerts for a node and that node is part of an app monitor, will the mute also apply to the app monitor or do you have to UNMANAGE the node?

Also, if you UNMANAGE the node, do you have to go back into node management and manage it again?  I thought that it would automatically manage it when the schedule is done but I believe that when we did this before, I had to go back in and manage the nodes again.

Thanks.