Valpro wrote: »

Like whether the Dro'Mathra are a type of khajiit or a type of Spirit

I think the Dro-m'Athra are a sort of dark spirit (of Namiira, if I recall correctly) that can inhabit the bodies of Khajiit and turn them into Dro-m'Athra minions, or "bent cats". I remember reading somewhere that there was this "bent dance" that was a sort of curse and anyone who watched it would become bent themselves.

Valpro wrote: »

If the Mane gets new powers from the title (like the green lady and what not)

I'm not too familiar with the lore of the Bosmer, but the way we see the new Silvenar be chosen in ESO is by direct intervention from Yffre. On the other hand, I think the current Green Lady says that she's the daughter or granddaughter of the first Green Lady you met on Khenarthi's Roost. So perhaps it's mostly hereditary or it come about through direct intervention of Yffre. As for the Mane, that is a hereditary title sort of, in that whether you get it or not depends on when you were born. Manes are not chosen through family ties, but by the position and status of the moons at the time of their birth. Khajiit believe that there exists a third moon which appears very rarely and that, if a kitten is born while the moon is present, that they are destined to be the Mane. In the time it takes one such kitten to grow up and replace the old mane, they are called the Lunar Champion and are taught in shrines and monasteries various things about... Mane stuff, I suppose. There's also a theory that there is but one mane (Rid-Thar-ri'Datta) and all the other manes are actually Rid-Thar reincarnated, but I seriously doubt that as you can actually talk to the ghost of Rid-Thar-ri'Datta while there is a Mane around and while there are two Lunar Champions around. Quadruple personality disorder?

EDIT: I forgot to actually answer the question...
Once a Lunar Champion becomes the new Mane, they don't gain any special powers like the Bosmer leaders do. Rather, they become the spiritual leader of the Khajiit. Before the first mane, the Khajiit worshipped a pantheon similar to other races. There was Alkosh, Mara, Hermorah, and others, but once the first Mane came around he established the Two-Moons Path the old beliefs were, for the most part, abandoned and now the Mane became the leader and guide of the Khajiiti people in achieving and walking through the Two-Moons Path.So a Mane doesn't get any superpowers and they don't become a major political ruler or something (that stuff is mostly taken care of by local princes and clanmothers), but instead they are the religious leader (like the Pope for Christianity). This does give them some authority, of course, but it's not quite like the Green Lady and the Silvenar, who are the literal embodiments of their people's strength and will respectively.

Valpro wrote: »

as well as the their connection with the bosmer. Just any of the more obscure lore would help for my script.

According to the Khajiiti lore (Words of Clan Mother Ahnissi), the reason Khajiit come in many shapes and sizes is because Azurah (the one who created them) knows of a "secret" that allows her creations to do that. Yffer, on the other hand, doesn't know this secret (or rather, after learning about it, shouted it out loud so it was no longer a secret), so that its creations (the Bosmer) were just of one type. There is this mention of the Ooze in the Bosmer lore, after all, which supports this idea. As for the more general evolutionary connections, I'm pretty sure both the Khajiit and the Elves are part of the Ehlnofey family, so they are somewhat related (I bet one hella drunk elf shagged a sabrecat and boom we've got Khajiit)