"I bumped into my good friend in the park."
At least 我在公园遇到了我好朋友 has to work! You definitely have a personal binding to good friends!
No, since location comes in the beginning in Chinese. Either before or after the person doing the action.
This mistake sounds like you say I bumped into in the park my good friend. Weird.
I dont think so because the location/preposition stuff is usually before the predicate
好朋友 good friend 很(要)好的朋友 bff, buddy
很好的朋友 is okay for speaking, but it's wrong in grammar. 很好的 are used for describing the personality, not the intamacy.
Am I correct in thinking “我在公园遇到我的好朋友了。” should be accepted? I thought you could put "了“ at the end of the sentence to indicate past tense.
The origin one is talking what happened in the past, and emphasizing on I. But if you put 了 in the end, it sounds like you wanna talk about what happened after you bumped into your friend. Though it's correct sentence, to native speaker the talking is not finished yet, we will expect the following thing.