I am going to assume that "you" are the character that is trying to stabilize the other.
You do not provoke an opportunity attack
The only thing in D&D 5e that provokes an opportunity attack is leaving an enemy's reach.
You can make an opportunity attack when a hostile creature that you can see moves out of your reach. (PHB)
Using your action to stabilize a creature is not movement at all and thus will not provoke an OA.
It does not matter where you are or how many other player characters there are, conscious or otherwise.
Attacks are (probably) not made at advantage
Nowhere in the rules for stabilizing a creature does it say anything about attacks being at advantage against that creature. In fact nothing suggests this would be the case.
You can use your action to administer first aid to an unconscious creature and attempt to stabilize it, which requires a successful DC 10 Wisdom (Medicine) check. (PHB)
Conditions that allow an enemy to have advantage are well spelled out in an ability or spell or determined by the DM:
Sometimes a special ability or spell tells you that you have advantage or disadvantage on an ability check, a saving throw, or an attack roll. [...] You usually gain advantage or disadvantage through the use of special abilities, actions, or spells. Inspiration can also give a character advantage... The DM can also decide that circumstances influence a roll in one direction or the other and grant advantage or impose disadvantage as a result. (PHB)
So no abilities that you have used in the example would cause attacks against you to have advantage. The DM however might decide that they do because of the circumstances of the fight, but most like they would tell you if this were the case.