If you use "a" ("ao parque") you mean you are going there and will soon return, but using "para" ("para o parque", or informally, "pro parque") implies you are going there for a long time. In colloquial Portuguese this distinction is not made, or the idea of "for a long time" is really flexible, and "para" is often used where you wouldn't expect it to be used.
Yes, Portuguese and English verb tenses aren't exactly the same. Portuguese uses the progressive (-ing =-ando/-endo/indo) tense only when the person is actually doing the action at that very moment. English progressive tense is used for both present and near future, like you said.