When you create a block in views, the view itself already has a name (used for administrative purposes) and the block generally also has a title (shown to end-users). So when you want to give the Block a name (under Block Settings, displayed in the admin interface), rather than typing in something new (or repeated), I'd also like the option to use the existing view name or block title.
So I propose adding radio buttons with those options (and also a 'No name' option) as per the following screenshot/mock-up:
(obviously the textfield will be hidden when one of the other radio buttons is selected)
Recent comments
You can use Rules or the Node Notify module for comments. When a new account is created, I believe there are Rules to send.
Email notifications
There's a few way to accomplish it, but it really depends on your full requirements. I'm working on a contact management module but it won't be released for a few months. There...
Pairing fields
I'm fairly sure that some people have done this successfully in Backdrop. Please can you list the modules you are using; that should help us get the right people to join this conversation.
How to render facet blocks?