Do cold baths in the sea improve sciatica pain?

Possible. It can make you feel the cold more than the sciatica in a way tricking your brain into believing the sciatica pain is gone. If that works, wonderful. Likely it will only last until you warm up at which point the pain may return. If you are not getting relief, I would suggest seeing a pain/spine specialist for other options.
sometimes. Depending on the cause of sciatica and your particular symptoms, aquatherapy may help with your pain by relieving the stress in your spine.
Doubtful. Can't hurt, but no medical benefit i would surmise from the treatment. Potentially, if cold enough, could create an anti-inflammatory effect. However, i believe hypothermia would be the more likely outcome if that cold.