what mass of hydrogen chloride gas is required to produce 250 ml of hydrochloric acid solution with a pH of 1.57

Answer 1

You were right on the (H^+) = 10^-1.57 = 0.027 mols/L.But wrong on the rest of it.
You want 0.027 mols/L so you will need 1/4 that for mols in 250 mL or
0.027 x (250 mL/1000 mL) = 0.0069
Then mols = grams/molar mass.
You know molar mass and mols, solve for grams. I estimated that 0.0069 so you may want to start over and redo it more accurately.