Which structure is correct?

We won at/in that tournament.

Are you participating at/in that tournament?

The correct preposition in both sentence is "in."

The preposition "at" could also be used in the first sentence.

Either "at" or "in" could be used in the first one?

Yes, it could! But "in" is probably the better choice. A tournament takes place at a specific location, so "at" might be appropriate.

Yes.

To determine the correct preposition to use in these sentences, you need to consider the context and meaning.

1) "We won at/in that tournament."
Both "at" and "in" can be used in this context, depending on the intended meaning.

- "We won at that tournament" suggests that the victory took place at the location of the tournament. For example, it could imply that you won the final match or achieved success during the tournament.
- "We won in that tournament" implies that you emerged as the overall winners of the tournament. It emphasizes that you were the champions of the entire event.

2) "Are you participating at/in that tournament?"
Similar to the previous sentence, both "at" and "in" can be used in this context, based on the intended meaning.

- "Are you participating at that tournament?" indicates that the person is physically present at the location of the tournament and actively taking part in it.
- "Are you participating in that tournament?" implies that the person is involved or included in the tournament, regardless of the physical location. It might refer to their participation as part of a team, as a player, or in a different capacity.

In summary, the choice between "at" and "in" depends on whether you want to emphasize the location or the overall involvement in the tournament.