Does spitting up mean my child is teething?

No. Spitting up may mean a lot of things, from "nothing" to overfeeding to a whole bunch of possible problems, but it has absolutely nothing to do with teething.
No. Spitting up is not a symptom associated with teething. It could be from something as benign as overfeeding to something more serious. Discuss this with your pediatrician.
No. No, spitting usually has nothing to do with teething. Many babies will spit up normally, and it is nothing to worry about. I would only worry if your baby isn't gaining weight or very fussy with their spitting up.
Absolutely UNRELATED. One has nothing to do with the other.
No. Spitting up is a normal affect of a developing gastrointestinal system. It is probably independent of teething.