I don't think that Hitler's rise to power was democratic, but my reasons are different.
1. Prime ministers and Chancellors (largely the same) are not elected as such, but approved by a majority of the legislature. So while technically Hitler was not elected in the capacity of chancellor, his appointment was legal on paper. As said, most of the things he did afterwards were unconstitutional.
2. See number 1. The conservatives approved his bid for chancellor because they didn't believe things would turn out that bad in practice. This isn't an unusual turn of events in parliamentary democracies today.
3. No argument.
4. I think that it's actually unknown what the truth is behind the Reichstag fire. It could be that it was a false flag operation orchestrated by the nazis, or it could have been a lucky turn of events that gave them the excuse they needed to cement their power.
5 & 6: I agree with you, and these are the reasons why I don't think that the rise of the nazis qualifies as "democractic".
The Weimar Republic never had one easy moment from its inception, and having paramilitary gangs like the SA mucking things up only made it worse. The various factions in the Reichstag were never able to form a coaltion to actually support a government, at least not for any meaningful amount of time. The only reason the administrations/cabinets functioned at all was because they used various "emergency clauses" to keep the daily operations of the state running. Which is one of the reasons why Hitler was able to shove aside the constitution so easily - because it never worked properly to begin with.
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