If I use a Move Action to move 30', and then use a Standard Action to cast a spell, I can still use the Counterspell Exploit (Immediate Action) to prevent an enemy spellcaster from casting right?
Because the Exploit works like dispel magic, I just want to make sure that there isn't a "can't cast more than one spell (the Standard Action spell, and the "Dispel Magic" exploit) in the same round type of restriction.
Nope, no restriction. You are fine doing what you are doing.