During the 9 days, is one allowed to shower in cold water without soap before and after the mikva?
Answer:
Before immersion in the mikva, when showering is a hygenic requirement, it is permitted to shower.
After the mikva, one should not shower, even with cold water, unless one finds the chlorine (or the dirty water) especically disturbing, in which case it would be permitted to shower (cold) in order to remove the dirt.
It is preferable to avoid washing the entire body together, but to wash limb by limb.