April is nice...highs in the low 60s, not a lot of fog. Just occasional rain. But yes, you'll need a jacket...you almost always need one on hand here, because the weather changes quickly.
Can you swim in the sea? Yes, but it's fairly cold and a lot of the open ocean areas have strong currents. There are a few sheltered place (Aquatic Park, notably) where you can safely swim.
Yes, you can get a sunburn. 😉
It's pretty safe in most places, including those that a visitor would go. But it's a city, so you do have to keep your wits about you.