It's perception with disadvantage to locate an invisible creature. Only exception is when there are clues to work off (ie. orc sees invisible PC by following footsteps on snow, here I'd make a regular perception or no roll), or it's location has been found and called out by others (no perception needed) and it hasn't moved.
Hide requires a stealth roll vs passive perception, but you don't disappear. It is still possible for a creature to find you if it changes position (ie. walks behind the wall you're at) or if it uses its action to find you (perception vs the result of a stealth roll). Because you're using passive perception, there are varying levels of success. It's easier to hide from a wolf than a dragon, for example.
Both give advantage on attacks made by the hidden/invisible creature. Both would require guessing squares if no location has been determined, and regardless of whether they are there or not you should make them roll for it at disadvantage. Do not calculate cover on AC unless it's relevant (ie. hiding behind bush).
Darkness could conceal creatures, but they also conceal your PCs. Regardless, most parties and many creatures have darkvision, so the efficacy of this beyond magical darkness is mixed. Blindvision helps, but comes with its own limitations. Noise can reveal location, yes, and stealth should prevent that if rolled well.
As always, you're free to modify any of this if you feel the mechanics are too light or punishing. But get a feel for it RAW first and adapt based on your play experience.