1) First to answer your specific case, Swarms are not affected by forced movement from ranged or melee attacks. If your warden's attack was a close burst or blast then I believe that RAW the swarm could be affected.
A swarm is composed of multiple creatures but functions as a single creature. A swarm can occupy the same space as another creature, and an enemy can enter a swarm’s space, which is difficult terrain. A swarm cannot be pulled, pushed, or slid by melee or ranged attacks. -Rules Compendium p. 316
2) To answer your more general question there's nothing rules as written covering aquatic creatures out of water in a general sense, so you could assume that if they only have a swim speed then they can't move once beached. Beyond that there's nothing that the rules cover so its up to the GM/DM. The only thing the aquatic keyword effects is in the quote below.
"Aquatic creatures can breathe underwater. In aquatic combat, an aquatic creature gains a +2 bonus to attack rolls against nonaquatic creatures." -Rules Compendium p.308