It doesn’t need to be remotely close to the noun lol

You can, but it isn’t that common, it’s even considered a form of hyperbaton (messing around with word order).

Note that those distinctions that you mentioned (subjunctive vs. indicative, the right negation, perfect vs. imperfect) are all handled through the morphology in Latin, not the syntax (as in English). And yes Latin morphology can get really crazy, just like Polish or any other “old style” Indo-European language.