Creating a Database of Characters

but my problem is what is a good program I could use to organize each character's bio.

I would recommend MySQL. I'm not sure if it's what you mean with 'program', but MySQL is very nice.

Also, what are some good methods of diversifying each character so they are completely different from one another, giving them their own identity. (Like a real person)

Like a real person? Then make them like a real person. That means give them reasonable personalities, skills, jobs, and back stories. I've proof read (I'm a proof reader in a happy little community) many stories where the characters aren't realistic. One of them is too good (too good into the point of ridiculously good), or too evil (trolling other characters for no single reason whatsoever).

Back story seems like the main factor to make your character unique. Back story determines the character's personalities. A character who had a happy and lovely past will be a good person, while a character who had a sad and hatred-full past will be a vengeful and evil person. That's very reasonable, but in some cases, a character who had bad past can be good.

Back story also determines the skills of a character. A character in a wealthy family may be more educated than a character who came from a poor and deprecated family.

Then, back story creates the motivation and fear of a character, and this is what makes characters different. It also makes conflicts. A character's back story creates its motivation and fear, likes and dislikes, etc.

Can two characters have the same back story? Even if they're twin characters, I doubt they will have the same back story. Then we can conclude that back story is what makes characters unique.

One advice: be reasonable.