1. He is in the river.

Question

[For example, half of his body is in the water. Or he is swimming in the river. He may be enjoying scub-diving in the river.]

2. He is on the river.
[He is rowing a boat on the river. He is floating down on a log on the river. He may be sitting on a boat on the river.]

3. He is at the river.
[He is not in the river, but he is by the river....Is my explanation right? Would you check them, please?]

Answer 1

Yes, all your explanations are right.

=)