I've never watched a daytime soap but have wondered:

Are they always new episodes for the whole year or do they have seasons like primetime shows? Do they rerun episodes?

New episodes all year.

Although on some holidays, especially on CBS they run "Classic" episodes where major events happened.

They also have breaks of varying lengths due to other programming commitments. For instance, the CBS ones get pre-empted for college championship tournament basketball.

They show new episodes yearlong, however the plots are all reruns.