Will a mosquito bite someone with a blood disease or can they sense that the blood is not healthy?

No they do not sense infections in their victims. Mosquitoes are capable of catching some diseases from humans, like a staph or strep infection, but they are mostly carriers only. They are known around the world as carriers for the disease malaria. But they are not capable of transmitting HIV from one person to another. The West Nile Virus is being spread by them and is one of the dangerous diseases in the world now.