"My children can now swim."
Translation:Mis hijos ya pueden nadar.
I translated this as: "Mis hijos saben nadar ahora." - This was accepted as well.
But yeah, I've also understood "ya" as already. But on the other hand, someone could think that "now", when talking about learning a skill, could maybe mean that they've now reached something "already" compared to where they started. I don't really know. Right now I cannot articulate my thoughts regarding this clearly; even to myself. Maybe someone will get what I think I'm trying to say. xD
It depends on the verb, for "poder" I don't think there's ever an "a" or "de." This page has a list of verbs that are directly followed by the second verb: http://spanish.about.com/od/infinitives/a/infinitives_after_verbs.htm
Here's a list of verbs that are followed by "de" http://spanish.about.com/od/infinitives/a/verb-de-infinitive.htm