Your hypothesis is mostly correct.
Hide in Plain Sight allows you to impose a -10 penalty to any roll made to detect you if you are successful in using the Hide action, as long as you remain motionless.
Vanish allows you to take the Hide action as a bonus action.
The Wood Elf racial trait Mask of the Wild allows you to take the Hide action even when only lightly obscured by natural phenomena.
Skulker allows you to take the Hide action when you are lightly obscured universally, so Mask of the Wild would become redundant, missing a ranged attack would not reveal your position and dim light would impose no disadvantage on your Wisdom (Perception).
I assume that the Sneak Attack comes from a multiclass into a Rogue.
Thus, you are mostly correct in your hypothesis: given your scenario, you may use your bonus action to take the Hide action. If you have remained motionless on that turn and further elect to not move for the rest of the turn, any creature attempting to detect you will have a -10 penalty imposed to its roll. RAI (rules as intended) I assume that bringing an arrow to bear violates being motionless. You may then make a ranged attack which will not reveal your position to the creature(s) you are attacking and/or hidden from, and if the creature(s) cannot see you due to you succeeding on being hidden from them (a successful Hide action), you will trigger the Rogue feature Sneak Attack due to having advantage on the attack. Once again, the -10 penalty to detect you is lost the moment you aim the bow and draw the arrow back.
It seems the problem you're trying to solve, is how to get consistent Advantage on attacks, without provoking opportunity attacks. This depends on a number of things.
What is the boss's reach? If the boss's reach is longer than 5 ft, then you will not provoke an opportunity attack to move behind your Dragonborn friend, if he is within 5 ft of the boss.
Must you use melee attacks? Using ranged weapons in a different location would be much safer, keeping you farther from the Boss, protecting you from Area of Effect spells or abilities, and giving you Advantage consistently without having to worry about disengaging.
You're also making a few assumptions:
- Hiding means you are completely undetectable. This is false. He can't currently see you, and you have advantage to hit the boss, but for an intelligent creature, it's pretty obvious you're behind the Dragonborn somewhere, and he can still move around your friend to spot you. Additionally, barring the Skulker feat, attacking will reveal you. Also, simply stepping out from behind the Dragonborn will reveal you if the Boss is looking in your direction. (Also note there are no facing rules in fifth edition by default, so this is subject to GM rulings) Note this makes hiding in melee rather impractical without specialized abilities.
- Nimbleness means you can stand in another creature's space. You may pass through another creature's space, but you may never end your turn in another creature's space, unless they are multiple size categories larger than you.
As it stands, the Rogue does not have enough actions to Disengage, Hide, AND Attack in one turn, so he would either provoke an opportunity attack, or not be able to attack. The alternative that would allow Advantage attacks every turn, is to use a ranged weapon, and hide at a distance.
Note, if all you're concerned with is getting your sneak attack bonus, all that is required is either having advantage or an allied creature is within 5 ft of your target. Keep in mind that applies to ranged or melee attacks: so as long as the Dragonborn is next to the boss, the Rogue will still get sneak attack against it.
Unseen Attackers and Targets (Fifth Edition SRD)
Combatants often try to escape their foes’ notice by hiding, casting the invisibility spell, or lurking in
darkness.
When you attack a target that you can’t see, you have disadvantage on
the attack roll. This is true whether you’re guessing the target’s
location or you’re targeting a creature you can hear but not see. If
the target isn’t in the location you targeted, you automatically miss,
but the GM typically just says that the attack missed, not whether you
guessed the target’s location correctly.
When a creature can’t see you, you have advantage on attack rolls
against it. If you are hidden—both unseen and unheard—when you make an
attack, you give away your location when the attack hits or misses.
Best Answer
Hiding takes an action
So, if the character is not able to attack solely using a bonus action or is allowed to hide as a bonus action he cannot hide after an attack.
Additionally in the PHB on p. 177 it says:
So you first have to get out of sight before taking the hide action.
For Wood Elves it is indeed possible when only "lightly obscured", but still he requires an action.
Also, just to clarify how being hidden works:
Even if you might say, that the target did not turn around and couldn't see the Monk, he will not stay hidden! I do not know if your player meant it that way, but for clarification in the PHB on pp. 194f under "Unseen Attackers and Targets" it clearly says, that you give away your location when the attack hits or misses. And after you gave away your location you must hide again to benefit from "Unseen Attackers and Targets"! Even if you are under the effect of "Greater Invisibility".