98 Cirrus Oil Leak

I suspect you mean the crank shaft oil seal is leaking and oil is getting onto the timing belt. You don't want to risk anything happening to the timing belt on this engine as that will lead to very expensive repairs to the cylinder head and valves. If you have been losing oil at a pretty good rate, get it fixed. If just a little spotting was noticed during a routine inspection, it might not be that serious. A second opinion might be in order. The estimate seems a little high but this is a rather difficult job on this model car. They are probably also going to replace that timing belt, (very wise idea at the mileage listed), and the water pump which helps hold the belt tight.

Sounds like they know what they're doing but as is often the problem with mechanics, verbal communication is not their strong point.

Everything they told you about the timing belt is fairly accurate, but if it breaks, the engine is not "worthless"; it simply will need expensive repairs. The best way to avoid that is by having the timing belt replaced well BEFORE it breaks. There is a recommended replacement interval spelled out in the owner's manual. Because of the potential for high-cost repairs, I wouldn't wait as long as that recommendation specifies.

Besides breaking, that belt can jump a few teeth on one sprocket. If it jumps only one tooth, the Check Engine light will turn on and there will be a diagnostic fault code stored in the Engine Computer's memory. Engine power will be down too. If the belt jumps two teeth, the computer will shut the engine down to protect it from damaging the valves. In that case, it will not start after cooling down as yours is doing. If the belt jumps three teeth, the moving pistons will hit any valves that are open and bend them. That's when things get expensive. When the belt completely breaks, some valves are wide open and as the pistons coast to a stop, they hit those valves and cause the damage.

Oil on the timing belt is never good, but it won't lead to immediate failure. Oil degrades rubber parts over time.

As for the stalling problem, and it restarts after a brief cooling period, that is the classic symptom of a failing crankshaft position sensor or camshaft position sensor. Oil on them is irrelevant because they work through magnetism. Dirt and oil don't affect their operation.

Regardless of who to believe about what causes which problem, at 107,000 miles, if the timing belt has never been replaced, get 'er done. That's cheap insurance to prevent costlier problems later. It is customary to replace the water pump too at the same time. Either the water pump OR the timing belt are fairly involved repairs and both require disassembling the same things so you might as well do both at the same time. Also, the water pump pulley is one of the idler pulleys that helps keep the timing belt tight and in alignment to prevent wear. NOT replacing it would be penny-wise and dollar-foolish.

I feel better about the estimate knowing it includes the water pump and timing belt. You might want to call around for a second estimate, but the first shop has more diagnostic time involved already so their estimate will likely be more accurate.