I know some weapon qualities activate with advantages, but only with successful hits. Are you allowing other results with no successes (like 2 advantages adding boost to someones next check, etc.)

Yes, spending advantages without successes is encouraged as it adds an interesting dimension to failed checks, this is called out in the text of the core book. Eg: the shot misses but distracts the goons adding a boost die to an ally's next check.

Also, some weapon qualities like blast can be activated even without a success, which can be a fun thing to spring on players.

That's one of the primary roles of advantage within the system. The point of Advantage and Threat is to change things from a binary "yes/no" result to include results such as "yes, and..." "yes, but...' "no, and..." and "no, but..."

If you restrict Advantages to successful rolls, you'll be doing yourself a grave disservice. If you want a specific rules reference, check page 23 of the core rulebook. It states in the section titled "Advantages and Threats" that "The possibility for a positive or negative side effect can occur regardless of whether the task succeeds or fails."

Yeah, I was pretty sure that was how it worked, just wanted verification. Thanks.