Which youkai group they have in mind? Will they be contracting the Eientei? Will, they also furthering certain contract as well once they have made them in order to acquire some sample of Gensokyo magic that they can safely study? Will TSAB be able to advance their magic and tech enough in the future to match Gensokyo youkai without the need of super big guns?
The Tengu will handle negotiations, at least initially - they're the most organized, can interact with humans fairly easily, and have the most
desire to do so. Whether other youkai/groups conduct their own negotiations will depend on what each side wants. Eientei won't do contract work; if people go
there they'll help them, but they won't leave Gensokyo - although they also don't particularly care about the provenance of their patients.
Nanoha-verse magic/tech already, in some ways, matches or exceeds Gensokyo youkai. The systems are different, however, with different rules and (dis)advantages, and your typical Enforcer is already capable of entering Gensokyo and being perfectly fine so long as he doesn't actually tick off the local big guns. The local bigshots - the Scarlets, Yuuka, Shinki - are unlikely to ever be matched short of entire teams of S+-ranked Mages, but they are extremely exceptional individuals.
What will the TSAB thinks of the Jewel Seed Replica that Remilia makes for Nanoha that allow using her full power without side effect? Will they be able to replicate it?
I'm not sure what you're talking about here.
Lancer was at the party because of Remilia's wants, not because of his. Illya was apprehensively appreciative of the Cards, due to them being what they are and her attitude being what it is; Miyu greatly appreciated the formulae; and Tohsaka and Luvia were very happy until they realized the implications of a master mage basically throwing away an awful lot of top-quality gemstones.
@Entropy Judge I have but one question for you. Whatever happened to Mami's severed head, that Flandre collected way back in the quest?
She still has it. Eventually, she will probably remove all the tissue, clean the skull, and add it to a collection; or she might just bury it somewhere.
So, what IS Candeloro's eventual fate?
And the magical girls who chose to migrate to Gensokyo presumably have their grief seed needs met by magic right?
Candeloro depends on whether or not the Mansion residents find a use for her. On her own, she will be content to remain in her barrier, nabbing humans as needed - but her attitude and cares conflict with Gensokyo's principles (like Gensokyoans being protected) and she doesn't care enough to help with anything. So Eiki's recommendation will be that she isn't fit for Gensokyo, which means she will either be killed or ejected into the Outside World (where she will be perfectly content), unless someone in the Mansion is willing to put forth the effort into civilizing her and making her comply with Gensokyo's rules, which will probably only happen if someone wants something that she can do.
Yes, Kyouko and Homura's Grief levels are being managed by Patchouli and Deis.