The only thing that could cause the tube to flex would be for either the engine or radiator to move - and if it's happening when the engine is revved, it would most likely be the engine moving. Unless it's causing a leak that can't be fixed by a slightly longer hose, don't worry about it - that's why the hose is made of a flexible material.
Yes
Yes. Your Check Engine light or Service Engine Soon light.
Could be, worn bearing/seal in water pump, loose hose clamp, faulty hose, faulty radiator, faulty gaskets, faulty heater core, faulty freeze plugs in engine block, faulty radiator cap, cracked cylinder head,
The coolant sensor moniters the coolant temperature. A faulty thermostat could cause the engine to run cool.
A faulty gas cap could cause the check engine light to come on but it would not cause a rough idle or engine noises. Start with having your local auto parts store read the codes. The codes will help determine why the check engine light is on.
Yes. IT can make the engine run to rich, and then cause misfires
It won't hurt the engine, But it can cause it not to run are even start.
A faulty muffler will not cause this but a clogged catalytic converter will.
Faulty engine
Faulty thermostat.
Not that I know of.
Yes, sometimes a faulty ignition switch can cause the engine to not fire. Also, a bad spark park can the engine to not fire.