In which condition(s) can I get this reaction:

Question

Fe + H2SO4 = Fe2(SO4)3 + H2

Answer 1

You want to oxidize Fe directly from zero state to +3 state, and reduce the H+1 to zero.

So look at the REdox potentials.
http://chemwiki.ucdavis.edu/Analytical_Chemistry/Electrochemistry/Using_Redox_Potentials_to_Predict_the_Feasibility_of_Reactions