1) Do you let them hide in combat? As?
Yes, provided they take the Hide action and they are either behind full cover or heavily obscured from the enemy. (As a house rule I also allow them to hide behind three quarters cover in light obscurement.)
2) If someone is hiding behind a full cover and leaves the corner to attack someone, does he attack directly with advantage (because it's hidden), or can you get a new stealth check?
In my game, to get advantage from your attack while hidden, you have to first get a fix on your target. After all, while you've been behind full cover, your target may have moved elsewhere or gone into hiding itself. So you need to peek or peer around the cover. This means you no longer have full cover, but three quarters cover instead and I allow your enemy a chance to see you in this situation (usually with a -5 penalty to their Perception check). If they spot you, you are no longer hidden when you make the attack and so don't benefit from advantage on your attack roll. You can peek around cover in this way without using any movement (ie while staying in the same five foot square/ space).
If the enemy saw you go into hiding behind that corner and is expecting to see you there, they get a +5 bonus to their Perception check.
If you actually move into a space that has no cover from your enemy and you are not obscured from them, then they can see you clearly, you are no longer hidden, and you lose advantage from your attack roll.
3) How do you apply the rule for stealth? And in terms of handling? .. Do you let someone sneak behind and try to steal a backpack for ex?
When you want to hide or be stealthy, you declare it. From that point on you are
hiding. When the time comes to contest your Stealth check with an enemy's Perception check, that is when you actually roll your check, and not a moment sooner! Your check result applies until you come out of hiding or you are spotted by a creature that you're hiding from.
If you are sneaking past a creature that is also sneaking or somehow imperceptible to you, then I will roll behind the screen to see who notices who. You and the other creature might sneak right past each other and never know that the other one was there!
I do let characters and other creatures sneak up on each other, but it's usually pretty hard. All the requirements for hiding still need to be met. In combat a creature is usually aware of all other combatants and their positions, but I might rule that it can be distracted, eg by the Help action, or if two or more of its enemies are adjacent to one another and to it ('up in its face' in modern parlance).
Out of combat, a distracted creature that is not moving takes disadvantage to its Perception checks. If it's moving, it cannot be distracted on Perception checks to notice a creature in front of it, but it can be in its flanks and rear.
If you attempt to sneak up on a creature
out of combat, you must roll a new Stealth check every time you halve the distance between yourself and the creature since your last Stealth check (eg if I am 90 feet from you and I'm sneaking up towards you, I must make a new Stealth check when I get to 45 feet from you, then again at 20, 10 and 5 feet).
If you attempt to sneak up on a creature
in combat, you must roll a new Stealth check any time you halve the distance between yourself and the creature since the beginning of your turn (eg if I am 90 feet from you and I'm sneaking up towards you at 20 feet per turn, I don't need to make a new Stealth check until I start my turn 30 feet from you; before I step into the space 15 feet from you, I make a new Stealth check.
4) Use facing rule (side of vision) to hide?
I don't use it in combat, though in certain circumstances a creature can be distracted in its rear and flanks, as described above.
5) Let someone hiding from hiding using stealth in combat?
Sorry, I don't understand what you mean.