While he did write mostly descriptive stuff, and much of his prescriptive stuff changed over time, he DID have "ought"-opinions on most of the stuff OP asks about.
>so marx supported state socialism
In the immediate, Marx supported something like the Paris Commune. You could definitely call that state socialism, albeit local and radical-democratic (Civil War in France).
In a more general sense, Marx supported the legitimate authority in the hands of the proletariat, the dictatorship of the proletariat (over the bourgeoisie), that is, as long as "proletariat" and "bourgeoisie" remain meaningful categories (Letter to Weydemeyer; Critique of the Gotha programme). That could mean some kind of state.
In the long run, it's less clear, and usually people go to Engels for that stuff: "withering away".
Apparently Marx intended a later volume of Capital to be about the state, but it was not to be.
>he was an egalitarian?
This depends on what you mean by egalitarian, but he argued forcefully against a form of "equality of outcome" immediately under socialism:
"Accordingly, the individual producer receives back from society – after the deductions have been made – exactly what he gives to it. What he has given to it is his individual quantum of labor." (Critique of the Gotha programme).
...instead arguing for some kind of labour voucher system, with equal compensation for equal work:
For example, the social working day consists of the sum of the individual hours of work; the individual labor time of the individual producer is the part of the social working day contributed by him, his share in it. He receives a certificate from society that he has furnished such-and-such an amount of labor (after deducting his labor for the common funds); and with this certificate, he draws from the social stock of means of consumption as much as the same amount of labor cost. The same amount of labor which he has given to society in one form, he receives back in another." (Ibid.)
Of course, in the long run, it would be "from each according to his ability, to each according to his needs".
Call that whatever you will. He himself goes on to think aloud about the equality-semantics of it all.
>he wanted a stateless classless society?
Classless, yes, as he states throughout his writings. As for 'stateless', see above.
>anarchism
No, though sometimes he and anarchists agreed on specific points, and they all supported and pointed to the paris commune.
>abolition of oppressive hierarchies?
It certainly seems like a "dictatorship of the proletariat" would be pretty oppressive towards its enemies, although at the hands of the masses. The paris commune also certainly had chains of command.
Afaik he didn't particularly talk about "oppressive hierarchies" in the general (and why would he?).
In the long run he did, however, talk about abolishing things like the "enslaving subordination of the individual to the division of labor" (Ibid.).