[RPG] Does a Warforged receive all the benefits of a long rest while wearing armor

Short answer: No, there are currently no rules about what happens if you sleep in armour. The are rules about how fast you can don and doff armour [pg. 146 PHB] that's quite kind and fast (you do not don full plate in only ten minutes in real life) so characters shouldn't really have any issues with switching in and out of armour.

The are however rules for swimming in armour. Page 183 in PHB under the heading Suffocating. It's what you use to simulate drowning which is what happens if you try to swim in armour, especially the sort made primarily of metal.

Long answer: Sleeping in armour while not ideal or the perfect recipe for a great night's rest isn't as bad as you'd think. Anyone who ever played hockey or American football knows that laying down and rest in all that padding and equipment isn't bad. People all through history have actually slept and spend long times, sometimes months at the time, pretty much constantly wearing armour both day and night. The great siege at of Malta is one such example. Another example though a non-combat one, is how the moon astronauts slept in their space suits during breaks between the moon walks. Even now modern soldiers are sleeping while wearing body armour.

Now some might point out that modern battlefield body armour is designed to be comfortable. But that's just it. All armour through the ages has been designed to be comfortable to wear, to move in and to rest in because otherwise no one would be able to use it during long periods of combat. Full plate is both agile, flexible and feels light to wear. Second thing to think about is that humans are adaptable and can learn to endure the harshest conditions (can't speak for those poncey elves though). The human brain can actually tune out things it finds annoying or distracting over time. So even if it is uncomfortably to wear armour you forget it after awhile.

Which bring me to my point. (Finally right.)

If the reason you want rules for sleeping in armour is realism you don't really need rules as the effect of a night in armour would be negligible for a fit person trained in wearing armour. You might give the players a disadvantage for the first roll they make after waking up if they make sleeping in armour a habit. But the truth is that the cold, wet and fear of sleeping outside in a dangerous situation have much greater impact on how well rested you are than if you sleep in your armour or not.

However, while sleeping in your armour might not be that bad for your rest, prolonged armour use without breaks will eventually lead to all manners of unpleasant side effects. For example there is something called pressure ulcers also known as bedsores. They are incredible painful and nasty. Another nasty effect is spinal compression.

Now there might not be any rules for those effects either though if they were they would most like be in the form of sickness and injury than anything else. Still, Google some images of bed sores and show your players and they might start removing their armour a bit more often.

It doesn't say it counts as armor or natural armor or anything, so it doesn't. It's just 1 AC on top of everything else, to emphasize the sturdiness of Warforged. It should stack with everything and prohibit nothing.

To support this, note that the Warforged trait provides a bonus to AC, rather than setting it to a number, as armor is wont to do. The Tortle, another race with an armor-related ability, sets its armor class to 17 like armor usually does, and correspondingly disallows further benefits from wearing armor, further illustrating that abilities that provide bonuses to the class of worn armor (like the Warforged trait) are not armor and are intended to modify armor, while abilities that provide a different default armor class probably count as armor and definitely don't modify the effective class of worn armor.