My mucus is a deep yellowish green, did my cold give rise to a bacterial sinus infection?

Maybe. One of the common myths about the common cold is that any yellow or green mucous means there is a bacterial infection present. All viral upper respiratory infections (colds) can make yellow mucous even without bacteria. The predominant feature is time and change. If you have had a cold for longer than 7-10 days, or if suddenly you develop thicker mucous after seeming to get better, its possible.
It depends... Many studies have concluded that the color of one's mucus cannot predict whether one has a bacterial infection or a viral infection. Statistically, most upper respiratory infections (uri's) are caused by viruses (the common cold). As a general rule, one should see a physician if your symptoms are progressively worsening.
Not necessarily. The association between the color of mucus and the presence of infection was removed long ago. Sinus infection would be defined by the presence of other symptoms - sore throat, headache, facial pains, earache, fatigue, chills, sweats, post nasal drip, achiness.
Maybe. You may have had your viral infection turn bacterial. The best way to find out is to have your doctor check you out. If it is only a very small amount of discolored mucus, it may clear on it's own, but if it has been going on for days, it is important to get it checked.