No likely but possible if coolant is leaking out onto some electrical component.
Yes, it can cause hard starting.
I blown head gasket can cause an engine miss which one cause a rough idle.
yes if its stuck closed.
Yes, I blown head gasket will definitely effect the emissions.
No, a normal tune up cannot cause a blown head gasket. A blown head gasket normally is caused by an engine overheating or by a defect in the gasket or head. If it happened right after a tune-up that is just a coincidence.
If it was a head gasket then the compresion would be low in the affected cylinders low compresion as a result of wear wil make the car hard to start and overheating can also lead to electrical problems, Besides blowing a head gasket, overheating can also cause a cylinder head ro crack. Low compression and engine not starting or hard to start are symptoms. As mentioned above, do not discard the possibility of electrical problems due to overheating. However, the prime suspects are blown head gasket and/or cracked cylinder head.
The first thing that comes to mind related to those symptoms is a blown head gasket.
yes
the answer is yes
No
It is not wise to drive with a blown head gasket. If you continue driving with a blown gasket, eventually your car will over heat and the engine will seize up. This can cause accidents if it occurs while driving.
The car will start but it will run rough and will probably overheat and cause worse problems.