How was the Gestapo formed and what was Germany's justification for it to the public? Was there any news coverage of its formation at the time-- if so what was the tone of that coverage? Who were the people joining this secret police force (demographics)? Upon it's creation, how and where were the Gestapo placed throughout Germany / occupied territory? What was the extent of what they were originally allowed to do in the beginning vs later, if any?
I can give you some information regarding the first question: "How was the gestapo formed and what was Germany's justification for it to the public" and about the people joining this police force.
Regarding the other question, i don't know enough yet to answer these questions.
The first and main reason the gestapo was established is because of the Fire in the Reichstag at the 28. February 1933. The gestapo came from the prussian polticial police force 1A. This police force, that was under the power of Hermann Göring (hitler called him in the cabinet as the Reichskommissar for the prussian interior ministry (that way he had access to the biggest police in the complete reich, he also became Minister president of prussia later). The gestapo was first established as the "Gestapa" on the 26. April 1933. Even though it was formally under the control of Hermann Göring the "Gestapas" first leader was Rudolf Diels. Diels was known for his knowledge about left extremism. Later the gestapa was renamed to gestapo. However regarding the people joining this gestapa it were mainly officials who have already worked in such areas in the times of the weimarer republic. Most of them were not fanatical nazis in the sense of their believe. Also it's important to note that most of them were working in offices collecting and sorting informations of resistance movements for example. Most of them were not acting as spies. Regarding the justification they basically said it was to further fight the (allegded) start of a communistic revolution. They recieved informations from a lot of different sources. First of all, their own research and already existing list of left-extremists from Weimarer Times. Secondly, social democrats and communist that couldn't resist the the torment and were revealing informations about their old party members. Later the gestapo also got a lot of their information, about for example political jokes, by their party members. Especially party members that had been in the NSDAP for long time were eager to report such stuff.
Some sources and interesting stuff to read;
Der Reichstagsbrand - Geschichte einer Provokation /PapyRossa by Alexander Bahar and Wilfried Kugel (i believe no english version sadly)
Burning the Reichstag: An investigation into the Tird Reich's Enduring Myster / Oxford Universy Press by Benjamin Carter Hett
and of course stuff such as
The Third Reich in Power/ The penguin Press by Richard J. Evans