Really didn't get the kathy Bates Character

Um, let's see now.
a) Why NOT make her a lesbian? Lesbians exist, they are usually quite political, and if this is a movie in which the politicians are supposed to be progressive and caring (at least in their early days) then it makes sense to have lesbians on your staff if only out of principle. THIS lesbian was also extremely capable - perhaps moreso than anyone else... so why NOT have her on your staff?
b) Perhaps the "sudden interest" of the young aide was lust? It happens, ya know? And the Kathy Bates character was also funny, smart, ballsy, and very attractive in many ways; why SHOULDN'T the aide be attracted to her, especially if she herself is perhaps lesbian? It is telling that you don't question why another one of the aids sleeps with Henry, but that a young aide could be sleeping with a LESBIAN...ooooooh! Goodness! (Time for you to grow up, honey!)
c) The suicide scene makes total sense. Just before she points to the moon and states that the moon is cold and distant and airless without the light of the sun. And she states that the Bill and Hillary characters were HER shining light. When they failed her integrity test, it meant that all the years she had spent working for them were worth NOTHING. And the light in her life had gone out; at that point, it is a perfectly logical moment for her to become suicidal.

"The answer to all these questions seems to be "Nothing / no reason. They're just trying to tittilate us."

- On the contrary, those aspects of the the film establish key points central to the theme, plot and character development:

"why make the kathy bates character a lesbian? What did that have to do with anything?"

- It cements the liberal element of the key characters, that they are Democrats and accepting of alternative lifestyles. They aren't racist either. Also, though Libby has strong convictions in her chosen candidate (that she supports with almost religious fervor and zeal), she isn't really moral in the purely Christian, biblical sense. Perhaps she can't live with herself because of that, as well as her other inner conflicts. She had been in a mental institution because she couldn't accept that Picker was less than perfect. She killed herself because Stanton and his wife utterly abandoned their past youthful ideals and were immediately willing to ruin Picker to win the nomination.

"What was the sudden interest of young aide Jennifer to become her lesbian lover?"

- It had a comic effect because the Billy Bob Thornton character "Richard" had previously expoosed his penis to Jennifer in front of everyone ("...gee I've never seen one that old before...", trying to bed her, but she rejected him. He had expressed an interest in "the one that looks like Winona Ryder" earlier, but Libby got her, and they were lesbians too. That a beautiful, young woman would attracted to Libby, an older woman by far, is probably vexing to Richard, a redneck heterosexual who "loves his mama". So it had a light sense of irony as well, in solidifying her utter disinterest in Richard, and in men as well.

"What did the end suicide scene add to the movie?"

- This was ABSOLUTELY key to the overall theme of the film and to Henry wanting to leave the campaign. Henry and Libby connected right away, as they both had "TB" ("True Believerism"). Libby could never reconcile the harsh reality of the contrast between human nature and the higher ideals of humans as they seek to become political leaders. This truth had first led her to being "...in and out of mental hospitals", and finally to suicide. She had alluded to her "graduation" when she tested the Stantons. They failed the test, and found herself ultimately unable to cope with the selfish nature of people and their willingness to do anything to win.

Earlier it had been established that she was "stable", which I think meant trustworthy, as she was ultimately the least stable of the bunch, despite all the craziness.

High ideals are constantly contrasted with human frailty and hypocrisy. The movie is a comedy, but is also a drama and a cynical in its view of political candidates. But it is fairly realistic as well...