Yes, it can cause hard starting.
The first thing that comes to mind related to those symptoms is a blown head gasket.
I blown head gasket can cause an engine miss which one cause a rough idle.
No likely but possible if coolant is leaking out onto some electrical component.
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.
The car will start but it will run rough and will probably overheat and cause worse problems.
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.
you have a blown head gasket water is getting in to the engine oil