When writing a sentence, Do you write, "So and so said...", or "So and So stated...." ?I always thought when using "said", you are paraphrasing...

Technically, neither.  I would use "says" or "states."

In formal academic writing (arts & sciences), you will say "says" (informal) or "states" (formal), or you may interchange the two if your discourse relies heavily on testimony.  Regardless, keep it simple and understated: the focus should not be on the lead-in sentence or the tag, but on the quote or paraphrase itself.

The reason it should be present tense is that the language of academia must be current and up-to-date.  Also, present tense suggests not only the past, but it connotes the future as well (that the idea is still relevant).  Even if you are discussing a novel written in 1960 about the 1930s, as The Autobiography of Malcolm X is, you will want to say, "Malcolm X says that the race problem in America is thus and so...".