Using nightbot on restream or use it at the same time on Mixer and twitch

You can multi-stream using whatever tool you want, but to use Nightbot across multiple platforms you will need to make an account for each platform and set it up for each platform separately.

So would I have to make a different screen name for say Mixer as already have Twitch linked and a 2nd email address?

Nightbot doesn't have a concept of unique emails or usernames across platforms. You just login to Nightbot with YouTube/Twitch/etc..