can sperm be alive in pool water? and can girl get pregnant if there is sperm in public pool ?

No — you can’t get pregnant from sperm in a swimming pool. Sperm can live outside the body for a short time under the right conditions, but those conditions aren’t found in water. There are a couple reasons why it’s hard for sperm to survive in water — not only are they all dispersed, but they’re also separated from the fluids that protect them. It’s also incredibly unlikely that any water containing live sperm would get inside the vagina.

If you were to have unprotected sex in a swimming pool, that would be a different story. But it isn’t possible for a woman to get pregnant from just swimming in a public pool.