Yes the best time to shower is soon after working out, preferably after a short cool-down time. Some people don't realize how strongly they smell after working out.
Yes. The answer is always yes. No one likes back pimples from wearing sweaty workout clothes.
I'd say it completely depends on how much you sweat. If I do 10-15 minutes of yoga and only break a little sweat in my face I don't take take a shower. I wash my face and then I'm good to go. If I get sweaty all over I take a shower of course.
Did you sweat> yes!
Do you possibly stink> yes!
Should you shower>YES!
Yes. Maybe you can do a hot-cold shower (i dont know the right english word for it(i'm from germany)). Where you often switch the temperature.