Monsters or players can have the ability to become invisible, as the spell. In the rules, it's said that an invisible creature gets advantage and enemy have disavantage.

p194 of PHB : 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 DM 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.

But the spell says that you lose invisibility when making an attack or casting a spell.

Invisibility : A creature you touch becomes invisible until the spell ends... The spell ends for a target that attacks or casts a spell.

1st question : so, does an invisible creature lose the advantage/desavantage when making an attack ? Or always have advantage for his attack, but loose disavantage versus an (opportunity) attack of the ennemy ? If he always have advantage, what's happened in case of multiattack ?

2nd question : in case of a pixie or a faery dragon who have superior invisibility, does the invisibility still remain ?

Superior Invisibility. As a bonus action, the dragon can magically turn invisible until its concentration ends (as if concentrating on a spell).

Note: you can attack without loosing concentration