Ok, i'll be careful here not to give "legal advise" because that could land me in some hot water. So first let me say, "consult with an attorney", and secondly let me say, that if you have a standard lease agreement, that yes, you can keep collecting rents while you look for tenants. However, once you have new tenants, the only amount the current lessees owe you are for the months they didn't pay while your unit was unoccupied. Now lets say, worst case, it takes you 2 months to secure new tenants, then legally you would only be able to sue for two months (check with your attorney). You would have to sue in small claims or special claims court.
Seond part: Yes, you are mandated by law to return the security deposit within 30 days in New Jersey (it may be different in Arizona) or else face the possibility of being sued for twice that amount. Now, if the tenants are breaking their lease, then you're entitled to hold onto that security deposit until you are able to get new renter(s) in that unit.
I am really flirting with legal advice here. Please note: that this is not intended to be legal advice and was provided based on my experiences in New Jersey. Your state laws may vary, and what i have described may or may not apply in Arizona. Please search your state's "landlord tenant laws" for more information.
I hope that helps. Please best answer it if you thought this was helpful.
PS These folks should really help you find a new tenant. Often thats making the best of a bad situation. No one gets hurt and everyone gets what he or she wants.