Is this correct?
 

How do you say, "Part of my family is Cuban and they taught me most of what I know," in spanish? Is it, "Parte de mi familia es cubana y ellos me enseñaron gran parte de lo que se," or, "Una parte de mi familia es cubana y ellos me enseñaron mucho de lo que sé."? Or is either okay?

Both are OK. The last version better captures what your English sentence says.
(You forgot to write an accent mark in the first translation.)

Welcome to the forums, by the way.

if you are trying to say exactly "they taught me most of what I know" shouldn't it be "ellos me enseñaron más de lo que sé"?

I think "Part of my family is Cuban and they taught me most of what I know," that "most" mean they taught me a lot of thing but not everything, so I translate: Parte de mi familia es cubana y me enseñaron casi todo lo que sé

Meaning they taught you 99% of you know but not 100%. Are you agree?

I think you should ask,

"Do you agree?"
or
"Are you in agreement?"

(Let's see if the English natives confirm...) :)

Don't you agree? :good::good:
Do you agree? :good:
Are you in agreement? :owl:

Ok, thanks!
I agree!
(I only have to nod in agreement here...) ;)