Grave Betrayal doesn't overwrite any previous colors or types. Rather, it adds another color and another creature type.

The phrase "with an additional +1/+1 counter on it" means that the creature enters with one more +1/+1 counter than it would normally enter with. It doesn't keep any counters it had on it when it died.

Each creature you don't control that dies causes a delayed triggered ability to trigger at the beginning of the next end step. If there are multiple such abilities, you can put them on the stack in any order. The creatures will return to the battlefield one at a time as each ability resolves. The last ability you put on the stack will be the first one to resolve.

In a multiplayer game, if more than one player controls a Grave Betrayal and a creature controlled by none of those players dies, each Grave Betrayal will create a delayed triggered ability at the beginning of the next end step. The first such ability to resolve will return the creature. Usually, this will be one controlled by the player furthest from the active player in turn order.

If a creature you don't control dies during the end step, that creature won't return to the battlefield until the beginning of the next end step.

If the creature card leaves the graveyard before the delayed triggered ability resolves, it won't return to the battlefield. This is also true if the card leaves the graveyard and returns to the graveyard before that ability resolves.

If the creature is normally colorless, it will simply be black. It won't be both black and colorless.