Yes, the police conducted a lawful search and seizure. An officer who has a reasonable suspicion that criminal activity may be happening, can stop and frisk a person for weapons to protect the officer's safety. The officers observed a person matching the height and weight of the suspects in the electronic store thefts, and further observed that the person leaving the electronic store was wearing a heavy overcoat on a hot sunny day. This would be sufficient for reasonable suspicion, thus the stop and frisk was lawful.
The suspect's Fourth Amendment rights were violated because a stop and frisk itself must be no more intrusive than what is necessary to discover a weapon to protect the officer's safety. Neither an iPod nor a digital camera feels like any kind of weapon, so the officer should not have removed them. If the .22 caliber gun had been discovered first, this would have provided probable cause for a crime to be underway and thereby justify a more extensive search. It is not clear from the facts whether or not carrying a concealed weapon is legal in Phoenix, AZ, if it is not then that would make the remaining search legal because carrying the weapon would confirm a criminal act.
The stop and frisk was reasonable, given the subject's odd behavior of wearing a heavy coat on a hot day. As discussed earlier, probable cause would only arise if the concealed carry was criminal in the jurisdiction. The facts do not permit an analysis of this factor. Assuming the act is unlawful, then probable cause existed. The main evidence that led me to the conclusion is the existence of the .22 caliber gun concealed on the subject. The arrest of the first suspect was conducted in a proper manner, so there was probable cause and the suspect agreed to the search. In the second arrest the police acted in an improper manner when they insisted on entering the home of the suspect and continually searching while a minor was present. The police should not have entered the home...