What is the proper position grammatically with adverbs in Spanish? Would I say, "Es importante que interprete los resultados correctamente" or "Es importante que interprete correctamente los resultados" etc?
Both are correct and grammatically and stylistically, (and both widely used) since the adverb modifies the verb, not the direct object (los resultados), so placement is not that relevant. It is grammatically possible to say "... que correctamente interprete los resultados", but this is not advisable. In any case, adverb placement is very flexible in Spanish. One of the few places where it cannot be used is between "haber" and a past participle, which is where English prefers to place adverbs (e.g. "never" in "I have never seen" cannot be placed there in Spanish).
Also, as another unrelated question, when I say "We will talk about..." would I say "Hablaremos de..." similar to pensar?
Quite, but the preposition "de" must be used instead.