I've added the notes everyone has made so far into the first post, but I'll need confirmation for the following.
Sphiel: You may have to talk to her twice before talking to Dogha...
Do you need twice? I managed with only once.
For Ouragan i dont know what to tell you, i remember looking around everywhere after Cragbark but coming up dry until i came back to HQ and got an event right after entering. Best i can suggest is going up to the top of HQ and hoping an event occurs, maybe talking to Icas and whoever else is up there, then re-entering.Maybe strip down like Biske suggested incase you have Icas in your party or something.
Apparently there's a timing requirement to complete Ouragan's final HQ event.
Ramin: After the attack on fort ark head to Salsabil/trade harbor for an event with ramin(maestro), Then head to HQ and accept the quest "Discordant Countermeasures". Then head to Naineneis/Main Street for another event, then cragbark/town square. After an event and a weak monster battle Ramin will join you.
You can actually do this much earlier after Shams joins, and by then the battle is probably a little tougher than a mere "weak monster", so beware.
Misrach: After the attack on fort ark head to Salsabil/royal Palace and talk to Misrach. After an event youll be taken to Mislato River and Misrach will join you. Note: You will most likely need to complete the quest "3rd Empress Consort Kureyah", making this character missable.
It's doubtful you can skip Kureyah's quest though.
Mourgent: The quest "Request from Gadburg" wont show up if Chrodechild is in your party(probably Fredegund, Meruvis, Yula, and Roberto too).
I know the event in the Nights' Veil residence won't happen if you've got any of these people in your party, but can anyone confirm if Gadburg's quest is not available if you've got any of these five people in your party? (It makes sense if Chrodechild and Yula are not allowed...)
Gilliam: You just have to talk to him(without logan works fine) after the fort arc attack. Then head back to HQ for the quest. After completing it go back to grayridge/outside ch hall and talk to him again to have him join you.
His quest is one of the few leader quests with alternative success conditions. Make sure you complete it successfully, not with a mere 100-potch reward.
@antimatzist: As far as i know he has to deny you atleast once. There might be some point where your able to recruit him once its passed, but im not positive on where(if i had to guess id say after the attack on fort arc, no later then when rarohenga appears). In another guide i read it suggested trying after every main story event, so if your still getting nothing, do a part of the story and try again.
I managed to get Namna the first time I got the dialogue options. I did make sure to visit him after every major plot mission though.