Does Repeat create two stacks on the chain once the card gets played, and can the opponent react in-between the two executions of the repeated spell?

No, Repeat does not create two separate stacks or chain items.

According to RiftJudge FAQ #4750 and Rule 746.1.d, Repeat appends the card's effect to itself on a single chain item. When you pay the Repeat cost, the spell is finalized as one single item on the chain that will execute its effect twice when it resolves.

Because it is a single chain item, there is no window for opponents to interact between the two executions.

Sequence of Events:

1. Playing the Card: You declare you are playing the spell and choose whether to pay the Repeat cost as an additional cost.
2. Finalizing: The spell is placed on the chain as one single item.
3. Opportunity to Respond: Your opponent now has the opportunity to respond to the spell (e.g., by playing a Defy or another reaction).
4. Resolution: Once the chain resolves and it is time for that spell to execute, it performs its effect twice in immediate succession with no interruption.

Important Nuances:

• Countering: If your opponent counters the spell (e.g., with Defy), the entire spell is countered, including the repeated portion. You cannot choose to Repeat after a Defy has been played.
• Choices: While the effect happens twice, you make choices for each execution separately (e.g., you can target two different units if the spell allows). These choices are made at the time the spell is played (Rule 746.2).
• Single Play: Even though the effect happens twice, the card is only considered "played" once (Rule 746.3.a).