The theory behind the titration by KMnO4 is that it is a self indicator and a good oxidizing agent. Oxidation by KMnO4 is the main cause of neutralization.
Nitric acid, being a strong oxidizing agent interferes with the oxidizing capacity of KMnO4, hence reducing the accuracy of titration. Similarly, HCl is also not used because Cl- ions will be oxidized by Potassium Permanganate, again reducing the effectiveness of titration. Also note that conc. H2SO4 is also not used because it is a strong oxidizing agent plus a strong dehydrating agent which interferes the volume in titration resulting poor accuracy. So, only DILUTE sulphuric acid is used.
I believe because HNO3 is an oxidizing agent and will oxidize Fe+2 to Fe+3.
Nitric acid does not make a reliably standardised solution because it tends to decompose on standing.In any lab you will see the brownish red fume over stored nitric acid.In addition of course the intense colour of the permanganate ion acts as an automatic end point indicator.