The Third Space Lord was a member of the Lords of Admiralty that controlled the Royal Manticoran Navy, in charge of the Bureau of Ships.
No idea. After Oyster Bay, I imagine many of the most senior and experienced candidates are already dead, so they may have to dig down for one here. I could see pulling in someone from the RHN or Beowulf's SDF here more easily than for a lot of other cases, assuming Grayson is equally hard-up for senior officers with relevant experience who could serve on loan. Shannon Foraker's Bolthole experience would serve the GA in good stead here, and it'd likely put her in a good position still to use her idea-hamster superpowers for Good.
Unless politics and rules have changed a lot. The Manticorian Space Lord positions are open only yo Manticore officers. Beowulf isn't a part of the SEM and the RH isn't either. The Grand Alliance is not a merging of those star nations, it's just an alliance. As far as I know the nations in it still have and will maintain their own economic, military and political independence. So naval officers from those navies won't be eligible for being a Manticorian Space lord unless they become Manticore citizens.