Minoxidil and Exercise; Does it mean that after this period I can shower or go for a running?

If the instruction says you shouldn't wash your hair 2 hours after using Rogaine, then don't wash your hair.  Showering is considered washing your hair, unless you are not wetting your hair.  Exercising or sweating is not considered washing your hair, unless you sweat so profusely it is washing away the medication.

Ideally minoxidil should be left on for 8 hours but the 'minimum' time I advise is 4-6 hours. After 4 hours, 75 % of the minoxidil is absorbed.This advice comes from a 1990 study. In that study, twenty-two healthy male volunteers completed a four-way, multiple-dose, randomized crossover study to determine the relationship between contact time of applied drug on the scalp and minoxidil absorption from a 2% topical solution. The researchers examined how much minoxidil is absorbed at 1 hr, 4 hr compared to 11.5 hours. Relative to the amount absorbed after a contact time of 11.5 h, absorption was approximately 50% complete by 1 h and greater than 75% complete by 4 h.Conclusion:Although minoxidil should ideally be left on 8 hours, tremendous benefit can still be achieved with 4 hour use. Understanding the absorption of minoxidil is important to help improve the ability of patients to 'stick with' the treatment. ReferenceFerry JJ et al. Relationship between contact time of applied dose and percutaneous absorption of minoxidil from a topical solution. J Pharm Sci 1990 Jun;79(6):483-6.

The point of using minoxidil, is to leave it on our head not wash it off after applying it. I generally tell patients to shower at night and then apply the minoxidil to the scalp, leaving it on all night and then showering in the morning to wash it out.