Synthetic and conventional oils are generally compatible with each other, and there should be no side effects. Although this would not be advised if it can be avoided. Each oil has its own mix of oils and additives that may not work to their full benefit if mixed with others.

Yes, there is a government requirement that all oils must have compatible additive packages to be certified. Just make sure it has the same certification as the synthetic you are mixing it with.

Yes. But if your car already has synthetic oil, do not switch over to regular. But if you're just topping it off, it will be perfectly fine

Yes, it is even sold mixed with conventional oil and is called a Blend.

Of course.