Translation:I will have a party on Friday.
I am still learning, thus there may be a better way than this, but I would use "every Friday" if i wanted to be explicit that I did this action on each friday, instead of just the single upcoming Friday.
"Every Friday" is 毎週金曜日 (まいしゅう きんようび, maishuu kin'youbi). 毎週 means "every week", so the whole saying is like "Fridays every week".
No, the basic meaning of あります is "to exist". It is true that 金よう日 に パーテイ が あります, which without context means "There is a party on Friday", with an implied 私は can express the idea that "I have a party on Friday" (technically "As for me, there is a party on Friday"), but that is in no way more correct than using します and saying 金よう日にパーティーをします. It is simply a matter of idiom that in Japanese you "do a party" when in English you "have a party".
Nothing says "we" or "I" specifically -- depending on context it could also be "he", "she", "they" etc -- but the を shows that the party is the object of the sentence, something one does, and not the subject. To say "The party is on Friday" you would say something like パーティーは金よう日にです (and for "There's a party on Friday" you would say 金よう日にパーティーがあります).