"Je vais à la" means "I am going to the" in English.
je crois que je vais faire la même chose means 'I think I will do the same' in English.
I am going to the bank
"je rentre à la maison" or "je vais à la maison"
"swimming" (sport's name) is called "la natation" in French. the swimming-pool is "la piscine" - I go swimming is "je vais à la piscine" or "je vais nager"
Je vais a la Paris.
I'm going to (visit) the beach today
"Je vais" means "I go." Example- Je vais à Montagne.
Je vais le (la) prendre.
Je vais être à la maison
Literally, it means: I am going to the washing up. I think you want to say "I am going to do the washing up." The term used is "faire la vaisselle" - to do the dishes. You can say, "Je fais la vaisselle". I am doing the dishes. Or "Je vais faire la vaisselle". I am going to do the dishes.
"je vais à l'école"