Can you pass on the cold/flu virus even if you haven't shown symptoms yet?

After the fever, I usually go through a coughing phase. It starts out fairly easy to cough out the phlegm. Afterwards, I feel much better and the coughing goes away mostly till the next morning. This can go on for several days, weeks, or months. When I get more stuff in my throat during the day, I start coughing again till I spit the junk out. Over time, the phlegm gets thinner and harder to cough out. My colds (I get 2 per year) always go the same way but vary in duration. Usually several days to several weeks. One time, I had a cough for over 2 months before it finally went away.

I know that the cold is caused by a virus and cannot be treated with antibiotics. Sometimes take cough suppressant medicine.

1) What is the stuff that you spit out? Contain dead virus?

2) Is the stuff you spit out contagious?

3)Is coughing (after you have had the fever) contagious?
3a)And, when the phlegm gets thinner, are you still contagious?

4)Can you still pass on the flu/cold virus even when you are not coughing?