Why is мимо not used with пройти here? Also, does "you will not" here mean "you are not to" (an order) or simple information: "Thanks for the instructons on how to get to your offiice. Will I be going by the park on the way? No, you won't pass there." (Also, "pass there" seems to me a rather awkward construction in English, but maybe it sounds more naural in Russian.)
Well, Russian пройти́ could indeed mean "to pass, to pass by", but I find it extremely unlikely that in the latter case is would used with там=there. That is, "пройти" = "pass by" or "move along" when it is used by itself or with "мимо" = "by (the side of something)":
Он прошёл мимо (меня) = He passed by (me) (presumably, without noticing).
It's not about motion per se. Туда describes direction or destination and thus usually requires motion (albeit you can simply look there), whereas там describes location but it does not preclude your movements at that location.
In case you are familiar with this word, туда=thither.