Can the Bountiful Luck halfling racial feat be used multiple times in one round?

Question

I play a halfling who has the Bountiful Luck racial feat (XGtE, p. 73-74):

When an ally you can see within 30 feet of you rolls a 1 on the d20 for an attack roll, an ability check, or a saving throw, you can use your reaction to let the ally reroll the die. The ally must use the new roll.

When you use this ability, you can't use your Lucky racial trait before the end of your next turn.

It is clear that giving a teamate a reroll means I can't reroll my own 1's on my next turn. But am I allowed to use the Bountiful Luck feat again for other allies before the end of my next turn?

Consider this chain of events:

1. Ally A rolls 1 on an attack on his turn. Bountiful luck grants a reroll.
2. Ally A rolls 1 on a bonus action check on the same turn.
3. Ally B rolls 1 on a save.
4. I roll 1 on a save on an enemy turn.
5. Ally C rolls 1 on a death save.
6. I roll 1 on an attack roll on my own turn.

From my understanding: The first ally definitely gets a reroll, and my own rolls definitely do not(4 and 6).

But numbers 2,3 and 5 are a little less clear to me. While the rule doesn't specifically disallow using it multiple times in a round, the limitation on the racial trait makes it feel like the intent is essentially "1 reroll per round".

Answer 1

You can only use Bountiful Luck once before the start of your next turn.

As you yourself have quoted (emphasis mine):

When an ally you can see within 30 feet of you rolls a 1 on the d20 for an attack roll, an ability check, or a saving throw, you can use your reaction to let the ally reroll the die.

And, as the Basic Rules of the game describe:

When you take a reaction, you can't take another one until the start of your next turn.

So, because you have to use your reaction you can't use Bountiful Luck again until the start of your next turn.

The description of the feat doesn't say anything about you needing to currently have the benefit from your lucky feature to use it. So if you have a reaction available, you can use it regardless of whether or not you have lost the benefit of your lucky trait due to a previous use.

You also can't use Bountiful Luck on yourself

This is discussed more in the question: Is a creature counted as its own ally?

Summarizing the answer here: the usage of the term "ally" throughout the game's rules, as well as its natural language definition, highly suggest that an ally is another friendly creature that isn't yourself. So, since you are not your own ally, you can never ever use Bountiful Luck on yourself. Even if the Lucky trait is active and you have your reaction.

Analyzing your chain of events:

1. Bountiful Luck grants reroll by using your reaction
2. You don't have a reaction left so you can't use Bountiful Luck again
3. You still don't have your reaction left, so you can't use Bountiful Luck
4. You can't ever use Bountiful Luck on yourself, and you are locked out of your Lucky trait because of the last time you used this feat. However, you can use Bountiful Luck on an ally at any point now because you have your reaction back. And the feat doesn't specify you need to have the Lucky trait active to use it.
5. You can use Bountiful Luck since you have a reaction (assuming Ally C's turn comes after yours and you didn't use it on your own turn)
6. You can't use Bountiful Luck on yourself ever. If you used Bountiful Luck since the last turn, you are out of luck (pun intended) since your Lucky trait is inactive for this turn.

Answer 2

Only one action (an Ally's) can benefit from your Bountiful Luck per Round

... you can use your reaction to let the ally reroll the die.

When you use this ability, you can't use your Lucky racial trait before the end of your next turn.

Your Ally re-rolling their dice is you using your Lucky racial trait.

Once you have used your Bountiful Luck in a Round, no matter who benefits from it, you may not use it again until after the end of your next turn.

Additionally, it uses your Reaction. Even if you were able to use your Lucky trait again, you would have to find an additional Reaction to 'fuel' it.