I really do recommend Richard J. Evans' trilogy on the topic, EXTREMELY detailed and well written. A bit long and expensive, but really worth it. All of what I'm about to tell is from them, so I hope you love history like I do and dive into the Nazi worldview like I did during that read.

A sociologist named Ernst Fraenkel wrote, in 1941, a book in which he describes the Dual State: the Normative State, delimited by the Constitution and Nazi laws, could (and would) be overrun at any time by the Prerrogative State, which delivered its legitimacy to the supralegal status of the Führer. Meaning, the Führer could step over the Constitution at any time he wanted; and that is considered not only a dictatorship, but a fascist government. There's your answer regarding the Reichstag: it existed, but since all other parties were eradicated or exiled (social democrats, communists) or forced to shut down (monarchists, liberals), the One Party State was controlled by the Nazi high-ranks.

However, there were lots of conflicts between in-state organs too: for example, the cultural area was disupted between Goebbels (Propagand Minister), Bernhard Rust (Education Minister) and Alfred Rosenberg (the Party's official ideologist). All of them wanted full control over orchestras, theatres, schools, radio and TV. As you are probably aware, Goebbels won that fight, and Rust was mostly powerless and discredited after that, which led to his downfall.

(Communist and Social Democrats, the largest leftist parties, were hunted down relentlessly, with heavy lossed on their sides, and many people tortured and murdered by the SA and SS during the first half of 1933. However, other parties were only threatened to suffer the same fate if they didn't obey and continued active, which worked: non-left parties shut themselves down for fear, and their ex-members were treated as normal citizens; ex-communists and ex-social democrats were marked by the regime, and any small mistake could lead to a concentration camp trip. Yes, concentration camps were initially created for them.)

One of the greatest crisis in the Nazi political system was the Long Knives Night. Nazi rise to power was mainly political maneuvers and populism, but after Hitler became Chancellor in 31 January 1933, started the actual fight over power; and no other institution was more important in that period than the paramilitary division of the NSDAP, the SA - Sturmabteilung (Assault Division).

The famous brown shirts were the ones who actually fought on the streets and took over Germany by force. During the first half of 1933, Germany was almost at civil war, with SA and SS officials taking over towns and deposing elected politicians. In Nazi terms, that was called the National Revolution.

In 1934, the SA was mostly used for showoffs and military parades, since there were no more internal enemies left to be defeated and the regime already had the actual military under their command. That was extremely frustrating for its leader, Ersnt Röhm, who had bigger plans for the SA. The low rank members were already craving for the blood and adrenaline of the street fights and violence from the 1920s. So, Röhm started calling out for the True Revolution, where the SA would continue the work they were created to do and begin the construction of a new Germany.

Of course Hitler would come to know that, and it enfuriated him. The SA were an actual threat to his newly consolidated power, with more than 4.5 million members (including the members of the Stahlhelm, when it merged with the SA in late 33) and thirst for blood. So, he used the SS to purge every single high rank official from the SA and destroyed their internal cohesion, to the point where more than 30% of members were forced to leave the organization by threats to their families and friends by the SS.

Well, when, after the Long Knives Night, the regime consolidated and Hitler had full power, a lot of changes started to happen. Basically, the political system became a pyramid, where decisions would come all the way from the top - Hitler, Göring and the high officials -, and low rank Nazis would execute them in the most psychologically-terrifying way possible.

Political power over the citizens of Germany were exerted by the Blockleiter (Block Leaders), commonly known as Blockwart (Block Wardens), in charge of the political supervision of the population in their city blocks. Anyone acting "suspiciously", meaning, in the Warden's eyes, trying to evade the (mandatory) "voluntary charities for the German Race", such as the Winterhilfswerk (Winter Relief), talking negatively about the regime or even making jokes about Hitler or NSDAP (Nazionalsozialistiche Deutsche Arbeiterpartei) members.

Block leaders could make people lose their jobs over not behaving accordingly, and some politically marked individuals, such as ex-communists and ex-social democrats, could even get to prison for small mistakes such as not donating to the Winter Relief.

TL;DR Nazi Germany was based over the legimitacy that came from the Führer, there were Block Leaders that controlled peoples' lives, the Reichstag was redundant and the power was within the high ranks.

Related, there are two terms I stumbled upon at the Mauthausen Concentration Camp museum that I haven't been able to find clear answers as to their meanings: a "Cabinet minister without portfolio" and "Gau capitals". My notes don't contain further information as to what they were referring to, my apologies. I wonder how they connected to the political system.