Can you play multiplayer with two computers from the same house sharing an ISP? Also with a 3ed person over the internet?
Yes and yes. You might have to force a different port on one, FS2NetD may not like it but you should always be able to add a custom IP and bypass using FS2NetD, assuming one of them has the proper port forwards set up to host. I have done two clients from one computer to a remote standalone and another client from another location. It's possible but not always painless. Busting through any firewalls with proper port forwards is probably the hard part though.
Can you using MediaVPs_2014 with FS2NetD now?
Yes, the current release of them is validated, however it required setting up another daemon. The FSU team hasn't released a patch yet, but adding "+server_port 12013" to your multi.cfg file will put you on the right FS2NetD daemon. Your games will be isolated from anyone not using that configuration, but your stock tables and missions should validate.
Is there any known remaining bugs in multiplayer?
What mission packs are multiplayer compatible?
Tried posting the entire validated mission list but that didn't work. Just realized the rest of my answer got cut off. There is all the retail multi missions, the multiplayer mission pack that hasn't been modified for years, the coop campaign, etc. Many of these were upgraded for the MediaVPs and are now validated on that daemon. I can send you the full list if you're interested or if you are curious about anything in particular just ask.
Are the latest multiplayer files included in the new installer app?
To my knowledge the multiplayer mission pack is part of the Java installer.
Does Babylon Project support multiplayer and does is work?
Also to the best of my knowledge, with the latest Zathras patch and the latest engine it has been tested for, TBP multi should still work fine.
Has Diaspora multiplayer updates been complete and tested?
I don't know specifics about the Diaspora multiplayer but it was working well at one point and should still be supported.
Any other unfinished multiplayer improvements in the works?
SquadWar is nearing completion, I need help getting the engine to communicate with SquadWar to validate mission and report outcomes. I'm working on an API to make that possible since it seems the engine used to communicate with SquadWar directly via PXO, and our FS2NetD implementation doesn't understand that, and I doubt it would be easy to do compared to what I'm thinking of. We've also been playing with the idea of implementing RakNet as the communication library to improve performance, starting with in-mission and perhaps replacing other components related to multiplayer as well. RakNet is modular so that should be feasible. But we need some more coders with a high interest in the multiplayer code willing to tackle this project. jg18 had expressed interest but is having trouble understanding our current net code.