Even if the engine dies,the steering wheel shoudnt lock as long as the key is still in the run position.Maybe it just feels that way due to the loss of power steering.Could be a loose or corroded connection at battery or alternater.The battery is only used to start the car then the alternater takes over the job of electrically powering everything.I would remove the battery and alternater and get a friend to take you to Autozone to test them.That way you'll knock out two birds with one stone.Check any fuses and relays related to the charging system too.Touch positive probe of multimeter,set on volts,to neg battery terminal and touch negative probe to neg battery post.Volts should read 0.2 volts max.Anything larger than this indicates a excessive voltage drop.Caused by loose connection,corroded end or cable,rusty connection,etc. Check positive battery terminal the same way.Remove neg battery cable,connect test light between neg terminal and neg post.If light is on,you have a short.
I would say it is neither. The battery light comes on because the engine dies. Something is killing the engine, but it is not likely to be the battery or alternator.
sounds more like a fuel issue.
