First, the large spring controls the engine speed when the engine is running above idle speed. The small spring controls the idle speed. Hence it is normal for the large spring to be relaxed at idle.
Second, the major kink in the cable inner near the governor's speed control lever, is supposed to be straight. That is why the speed control arm isn't being pushed all the way to idle. The kink may have been caused when someone tried too hard to push the control lever further, perhaps because the engine hadn't stopped.
Third, because it doesn't stop when you push the lever itself as far as possible in the stop direction, it looks as if there is a problem with either the kill switch, or the wire attached to the kill switch. As AVB said, if you have a multimeter ("VOM" in the US), check whether the contact on the moving arm touches the contact on the governor plate when you slide the speed control all the way towards slow. If you don't have a multimeter you have some extra work. Remove the cooling air cowl (top cover) from the engine and you will see the ignition module near the flywheel, at the end of the spark plug lead. Look at the module and you'll see a thin black wire running off to the kill switch. Trace the wire and see if it is connected at both ends: to the module, and to the kill switch. If it is properly connected, you'll need to check the module itself. You can do this by disconnecting the wire where it attaches to the kill switch, and with the engine running, ground that wire to a metal part of the engine. If the engine keeps running, and you're sure the wire is not broken internally and is connected to the module, your module is faulty.
