Nitration of pyrrole with sulfuric and nitric acids
Would 2,5-dinitropyrrole be a product of nitration of pyrrole with $\ce{H2SO4/HNO3}$?


I doubt it and would rather expect a lot of tar to be formed here. Pyrrole tends to undergo acid-catalyzed polymerization!

For decades, acetyl nitrate, formed by addition of fuming nitric acid to acetic anhydride, is the reagent of choice. 

Mononitration of pyrrole predominantly gives 2-nitropyrrole, accompanied by minor amounts of 3-nitropyrrole. (K.J. Morgan and D.P. Morrey, Tetrahedron, 1966, 22, 57–62. DOI). 

In the case of 1-methylpyrrole, the yield of the 3-nitropyrole is somewhat larger (H.J. Anderson, Canad. J. Chem, 1957, 35, 23–29). In you want even more of the 3-nitro isomer, a more bulky alkyl substituent (t-Bu) or N-silylation with $\ce{((CH3)CH)2SiCl}$ is a viable approach.

Nitration of 2-nitropyrrole at −15 °C with nitric acid in acetic anhydride  furnishes a 4:1 mixture of 2,4- and 2,5-dinitropyrrole with a total yield of 61%. (R. Alan Jones, Gerritt P. Bean, The Chemistry of Pyrroles: Organic Chemistry: A Series of Monographs, Vol. 34, Academic Press, p. 124)