well yes.

getting the blood to move and relaxing the body is essential and plus the moisture and heat can loosen phlegm.

and keeping clean really is a plus when you're suffering with germs from hell.

Yes as long as your home is warm and you dry of fully and wrap up afterwards, might actually make you feel a little better

Yes, totally

cold showers improve circulation , it might help you.

Hot showers help with loosening up mucous