For the most part, these concerns seem to me to be addressed in BT.

"Why, how, did he think the Nazi part was a good idea?"

In some of his comments, Heidegger seems to me to have thought of Hitler along the lines of Hegel's observing Napoleon ride past:

"I saw the Emperor – this world-soul – riding out of the city on reconnaissance. It is indeed a wonderful sensation to see such an individual, who, concentrated here at a single point, astride a horse, reaches out over the world and masters it.” - Hegel

In another passage from the link referenced by Path above, Heidegger writes:

"The world of our Volk and Reich is about to be transformed and everyone who has eyes with which to watch, ears with which to listen, and a heart to spur him into action will find himself captivated by genuine, deep excitement—once again, we are met with a great reality and with the pressure of having to build this reality into the spirit of the Reich and the secret mission of the German being […]"

In the Der Spiegel interview of 1966, we can find a sort of parallel I think between what he saw as his role as rector - bringing together the disparate sciences of the university (perhaps relatable to Husserl) and the Nazi's consolidation of power over the 22 parties apparently in conflict in Germany at that time.

From the interview:

"SPIEGEL: But we seem to perceive a new tone in your rectoral discourse, when, four months after Hitler's designation as Chancellor, you there talk about the "greatness and glory of this new era (Aufbruch)."

Heidegger: Yes, I was also convinced of it.

SPIEGEL: Could you explain that a little further?

Heidegger: Gladly. At that time I saw no other alternative. Amid the general confusion of opinion and political tendencies of 22 parties, it was necessary to find a national and, above all, social attitude, somewhat in the sense of Friederich Naumann's endeavor. I could cite, here, simply by way of example, a passage from Eduard Spranger that goes far beyond my rectoral address."

http://www.ditext.com/heidegger/interview.html

He also reportedly wrote to Karl Jaspers:

"What I report here can excuse nothing. Rather, it can explain how, when over the course of years what is virulently evil became manifest, my shame grew-the shame of directly or indirectly having been involved in it."

"Very poetic and very unphilosophical, I'd say."

I'm not familiar with that particular passage, but in some of H's later stuff, he seems to me to be attempting a kind of blend of the 'poetic' with the 'philosophical.' I think he does this because he views poetry as being capable of capturing a sense of certain things that cannot necessarily be named explicitly in philosophical prose.

"Heidegger never made something similar to a definition of the Being and even recognized that the Being is an indefinable concept."

I don't have the text in front of me, but thought I'd offer that in the beginning of BT, he gives at least one tentative definition of Being as "that which determines beings in their being," he suggests, as already noted, we already have a preontological understanding of being - ("what is being?" for example, presupposes a direction/horizon for the question and a sense of being in the "is" of the question we are asking), and from the start he repeatedly insists Being should not be thought of as 'a being,' and that Being can not be understood as 'objective presence' which is how philosophy/metaphysics has typically 'covered over/concealed' this character of Being.

I think a good way to think about this can be found in the beginning of Hegel's Phenomenology:
As soon as consciousness has a "this" or "now" or "here" for itself, the immediacy which it thought it had has already passed - what remains is the concept that has preserved/superseded and subsequently mediates.

Or in Heraclitus albeit with a different 'attunement:'
"No man ever steps in the same river twice, for it's not the same river and he's not the same man."

Heidegger discusses "being" a lot where Nietzsche thought it was a "vapor" and "mistake" --

I just thought I'd throw out there that as I recall, there is a footnote to the Stambaugh translation of BT in which Heidegger 'approves' of Nietzsche's characterization of being as a 'vapor' - I don't have a copy in front of me so can't cite the exact page/passage but thought it might be of interest.

Good points. In Heidegger's case, however, I just get the sense that yes, style matters so much so that for Heidegger's thought and project in Being and Time, it was crucial for him to write in such a way such that even his language and writing style themselves reflected what he was getting at - or to put it another way - it was crucial for him that the "form" and "content" of his style were as much as possible at one with one another lest his major points be lost on readers. Secondary readings and commentaries are definitely helpful, and from that point of view, one might be lead to suggest that he could have written that way himself to begin with - but then again we didn't get those secondary readings until later, and historically, it strikes me as a pointless argument. In particular, his style seems to me to be in line with his aim of overturning such things as "objective presence" in metaphysics, for example. Whether he could have written in another style while preserving this sense in his writing - well, maybe. But my point is I think he would agree that "style matters," and I think he had his own very much in mind as he was grappling with the ideas he was trying to articulate at the time. Also, for Heidegger, the relationship between being and language is far more intimate than say the relationship between a technical report and the stylistic concerns of lucidly transmitting and relating data or something like that. I think, too, that this aspect of his thought is a part of both his style in Being and Time and changes in his style in later writings.

Some philosophers and texts can be read outside a classroom. Perhaps all can - I imagine most, if not all can - but some a classroom/teacher(s) is/are helpful - or necessary. I think Hegel and Heidegger - and Kant - are best broached for the first time in a classroom setting. Also - In or out of a classroom - I think it's worth noting that even "philosophers" are just people - sometimes writing extraordinary things and sometimes in extraordinary circumstances. Read enough Anglo-American philosophy of mind and you won't get that vibe but the two figures you mentioned - Hegel and Heidegger - I'd say those would be the embodiment of such circumstances. Just people - but tackling extraordinary things and writing under extraordinary circumstances. And trying to fill big shoes - same as everyone else. So give them a break would be my second suggestion (first was reading in classroom setting if possible). As for his style - it's deliberate. If you think it's "unusual" or "atypical" - yes. Tough shit.