Tooth decay is damage to a tooth's surface, or enamel. It happens when bacteria from the plaque and biofilm in your mouth make acids that erode the enamel. If tooth decay is not treated, it can cause pain, infection, and even tooth loss.
Bleeding gums are a sign of gingivitis, or inflammation of the gums. Gingivitis is a common and mild form of gum disease caused by a buildup of plaque at the gumline. The bacterial plaque buildup at the gumline triggers an acute inflammatory response. This response causes increased blood flow to your gums bringing infection fighting cells to the area. This increased blood flow is what you see as bleeding gums.
Generalized teeth sensitivity is usually caused by thinning/worn enamel or gum recession. When the enamel is worn or the gums recede, the inner layer of your teeth, the dentin becomes exposed. Dentin is not hard like enamel and thus does have small nerve endings which when irritated, result in sensitivity or pain.