How can I trigger a custom event from my actors BP?

You could put an input that gets a reference to that player’s controller, fed by self on the event dispatcher or whatever means you are using to call your respawn function and use that to do different things based on which player was killed.

You’ll have to forgive me I’m not too up on the blueprint networking stuff, so I’m not going to be much help with that. You might be better served asking another question in the networking section specifically.

Glad to be of help with the first part though.