If those on the ship asked (Yonah 1:11) and Yonah answered (1:12) as far as how to save them, why did they ignore his suggestion (1:13)?
They didn't ignore his suggestion. This is how the pesukim go (according to Malbim):
1:12 — Yonah tells them that the storm is to punish him and not them, and since it's here to punish him for running away, they should throw him away so he can get his punishment.
1:13 — They reasoned that since the punishment is for running away, it would be more appropriate to return him there, but they weren't able because of the storm.
1:14 — They decided to throw him off, but first prayed to G-d not to count it as murder, since they had to throw him off to save their lives.
1:15 — They threw Yonah off.