Can a chigger bite affect the whole body?

Many bites. Chiggers usually jump onto a person from the grass and travel from the clothes onto exposed body parts. Their bites cause extreme itching due to chemicals released into the skin. You can get many bites covering the entire body if you're unlucky to walk into a cluster or nest of them. They can also be complicated by secondary bacterial infections which can spread systemically if not treated.
Unlikely. It would be unlikely to have systemic symptoms from one isolated chigger bite.