Can I swim without one or will it leak? Will it start leaking if I get out of the pool for a while? Would it be hard to remove if I wear a tampon? If I don't wear a tampon, will the blood stain my bathing suit?

Wear a tampon. It won't be any harder to remove than normal. If the pool/lake/ocean is colder than you are, plus you will be exerting yourself more than you would on land, the bleeding could become heavier. Nothing will leak if the tampon has been inserted correctly.