Ignition switch problem

Nope. That is actually designed to do that. The ignition switch tells the BCM "Hey I want to start the engine" The BCM then turns on a timer, it will activate the starter motor and keep it activated until the engine starts OR it times out. Most people do not notice it until something starts making the engine start hard or not start at all. Then suddenly they hear the starter keep turning even though they have released the key.

Most likely you need to have some tune up type work done like cleaning the throttle body and changing the plugs to get it to start faster and run better.

When you say it runs bad can you describe it or take a video and post it here?

Do the plugs and wires, if the mileage is correct they are probably worn out. Next run some seafoam through it to clean out the injectors. I would also put a scan tool on it that can read the misfire counters, that would tell you real quick if it was missing and on what cylinder(s)

Intake leak will cause a lot of problems. Any air that gets into the engine without going through the metering system will cause problems.

You might want to clean the throttle body as well. That can cause idle issues if it is all carboned up.