Either your timing belt is stripped or broken. In order to have compression the camshaft and valves need to be in time with the crankshaft. If it has a distributor cap then remove it and have someone crank the engine. If the rotor does not turn then the timing belt is bad.
Out of time.
no, the thermostat would have nothing to do with the car not starting.
If your car have very little or no compression it can cause you to lose horsepower.
Loose spark plugs would result in a loss of compression. This would make starting difficult and if the engine ran at all it would do so badly.
The intake and exhaust pushrods are different lengths. If you mix them up you can cause bent valves upon the first crank which would cause a no compression condition.
You will have to be more specific. Describe this strange sound.
Is your check engine light on?
Yes, it can cause hard starting.
no it will not unless the engine was extremely over heated destroying the compression
A fuel pump relay switch can cause your car to stall after starting. A malfunctioning fuel pump relay switch can cause your car to not start at all.
Could use more info such as make, model, engine and year.
It is probably missing. Have it tuned up and a compression test run on the engine.