Registering and sharing RELAYS between different pools

When registering stake pools, we specify our RELAY server addresses.

QUESTIONS:

  1. Exactly what’s the purpose of “registering” a relay? I understand what they do, but why must we “register” them?

  2. What happens if all my registered relays were down, and my BlockProducer node was connected only to other relays (which I run, but they aren’t “registered”)? Would I then be unable to produce blocks?

  3. Can the same node be registered for multiple stake pools? (if I ran multiple stake pools)

  4. What would happen if NO relays were registered, but my BP node still connected to my unregistered relays? (would I then be unable to produce blocks?)

I can only answer #3. Yes, you can have the same relays registered to multiple pools. I am curious about the answers to the other questions.