Many different things. You need to have a vet see your puppy to know for certain and to get the proper treatment for the puppy's rash.
it could be allergic or irritation to the kind of soap you used for the dog, or its something outside the puppy got into. also if it worsens i would recommend you don't use the same soap or take the puppy to your local vet.
He wanted to think things out carefully as he did not want to make a rash decision that could be costly.
The rubbing is probably because it itches. As to the nature, cause, and treatment of the rash, you'd better see a vet.
If you use an eyeliner that irritates your eye or that has irritating chemicals in it, and you use it every day it could make your eyes red and irritated but I don't think you can get an actual eyeliner rash.
You must take your child to a doctor to have this rash seen. Do not treat this rash on your own. There are many causes for rashes and there is no way to tell what kind of rash this is without taking your child to a doctor to have it checked. This could be serious!
because it might have lice or other bugs eating its head skin
He had a huge rash on his leg.
It could be heat rash from sweating.
No you should not go to school with a rash because it could be contagious
There are a number of conditions that could cause a full body rash with or without cold symptoms. This is a question for your pediatrician.
It could possibly be Lupus.
It sounds like you have a fungus and need a fungus cream.