Is scabies an infectious disease?

Yes, by transmission. Transmission of scabies is usually by direct contact. Parents to children, mom to infants is routine. Young adult usually by sexual contact.
Yes. Scabies is a disease caused by an ectoparasite mite. It is highly contagious.
Yes. The mite which secretes the agent causing the reaction is contagious.
Yes. Scabies is an Infectious Diseases caused by a eight legged mite that is less than 0.5 mm, It is very contagious by direct contact.
Yes. When we treat scabies, we know to also treat everyone in the same house as well as everyone with any significant contact even if they are not itchy. From the time a person gets the mite to the time they itch may be 2 months. Symptoms are due largely to development of allergy to the mites burrowed into the skin.
Sort of. The rash is caused by an allergy to the feces of a mite which is infecting the affected person's skin.