First of all make sure your battery has a charge and battery acid to full level , then check your battery connections, make sure they are all good and tight and clean. And it could also be your cables, mainly the positive
Not on a push mower that has no electric start. On a riding mower, yes there is an ignition key.
If it is a riding mower it may have a blown fuse. They are usually located near the solenoid.
There could be many reasons why your Sears riding lawn mower won' shut off. The key could be jammed for example.
its probly flooded.
It is a small electrical thing on the bottom of the carburetor. It will have one or two wires going to it. It shuts the fuel from getting through the carburetor when the key is off.
tractor supply has a key that fits...its less than 3 dollars
Pull start only
The kill switch is typically the ignition key. Depending on the mower it could also be a red push button labelled "emergency stop"
That is caused by too much gas getting into the engine after the key is turned off. If the mower is new enough to have a anti-backfire solenoid on the bottom of the carb then it must not be working. If it is an older mower and doesn't have one then the carb needs adjusting to back off the amount of gas.
Yes, you can replace the key with a switch/button combination. The key is mainly there as a anti-theft feature.
Your flywheel key might be sheared
Mine is built into the ignition switch. After you crank it turn the key back to the left slightly.