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.
yes if its stuck closed.
No likely but possible if coolant is leaking out onto some electrical component.
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.
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.
you have a blown head gasket water is getting in to the engine oil