Regarding standing still to avoid detection while invisible, IMO that is a significant part of what the hide action is about.
Exactly mate. Compare:
I'm not using Stealth. I'm just standing totally still to avoid detection while invisible.
I'm not using Athletics. I'm just competing in the track and field.
I'm not using Animal Handling. I'm just toilet training my dog.
I'm not using Deception. I'm just trying to convince the King of a whopper of a lie.
I'm not using Acrobatics. I'm just cartwheeling across a tightrope.
Im not using Intimidate. Im just threatening the merchant with a sword to his throat.
Players narrate the action. Its the DM that decides if there is a check involved, what the relevant Skill, Ability score and DC is if so, and if it takes an action or not.
Player (Steve): 'I move over to Bobs Rogue, and cast
invisibility on him.'
DM: 'Cool mate, you chant your spell and Bob disappears from sight (checks initiative order). OK, the Orc goes next. It swings its axe at you Bob.
Player (Bob): But I'm invisible!
DM: I know, but you need to remember that this is all happening more or less simultaneously. You havent even had a second of time yet since becoming invisible, to try and move from and obscure your location, keep quiet, cover your tracks and so forth. Heck; the Orc was more or less swinging his axe at the the same time as you vanished. Now the Orc is just swinging it in wide arcs hoping to hit something. (Rolls attack at disadvantage due to the invisible condition). He misses. Bob its now your turn.
Bob: 'Now that I'm invisible, I back away into the corner and stand totally still, quieting my breathing'
DM: 'Righteo mate - you can freely move this turn without attacks of opportunity because you're invisible, and the rules say the Orc cant make attacks of opportunity against a creature he cant see. You back off into the corner and take the Hide action. You're a second level Rogue so its only a bonus action for you. Roll me a Stealth check.'
Bob: (rolls) With expertise thats a 17
DM: Nice. You're totally hidden from the Orc (passive perception 10). He roars in frustration, and turns his attentions to Steves Wizard! Also, Bob, you still have an action remaining seeing as youve only moved and used your bonus action so far. What do you want to do?
Bob: I quietly draw my potion of healing and drink it...
And so forth. I mean its not hard.