I just want to put in a word for being cautious about calling something 'normal' or not. Humans are sexual beings from a very young age, and human sexuality is widely varied in terms of drives, appetites, and curiousity. Social norms define what is deviant, and American culture is pretty far on the end of the spectrum that says sex is taboo and inappropriate/bad/wicked/shameful in a lot of contexts, and there are only a few 'right' ways to express sexuality. For example, Germans have a long tradition freie koerper kultur (nudism). We have a book in German about body parts, and the last page is filled with SEVEN drawings of buck naked, anatomically intact kids, and the child is supposed to identify who is a boy and who is a girl, and there is a blank spot where he/she can draw in their own picture of themselves. So, merely posing this question to a German might elicit a different response than asking Americans or Australians.
I don't think the comparisons of penises, wanting to see what equipment little girls have, or saying, "Touch my butt!" is necessarily cause for saying his behavior is abnormal. Yes, it does lie outside the boundary of what American adults have delineated as appropriate, but I think almost all kids engage in some degree of exploration of their own and other kids' bodies between ages 4-7 or so.
Kids are not always good at reading boundaries between socially sanctioned and socially proscribed, and he has a lot of overlapping boundaries of public/private body parts (hands/penis), public/private spaces (living room/bedroom), public/private venues (school/home) to navigate. If he is very curious and doesn't have great impulse control, he may not be checking all of this stuff. Whatever is going on with him, I think it's important not to instill in him a lasting sense of shame if he is merely a very curious little boy. If it were my boy, I'd let him know that I appreciate that he is being honest with me, and let him know that he can ask me ANY questions he has about his body or other people's bodies, check out some books from the library about bodies and reproduction. We also talk a lot about manners and how manners are things we do or refrain from doing in order to make sure everyone around us feels comfortable and has an enjoyable time when we are with them. So, #1, it's very bad manners to ask other people to show us their private body parts. And #2, it's also very bad manners to get undressed when we are out in public or entertaining company.
Do you trust your therapist? If she has a good and ongoing relationship with your son, do you think she can read him well enough to know if this behavior is indicative of some deeper psychological disturbance or pathology? I would like to believe that human beings are resilient enough that if he was hurt at a daycare at age 2, taken out of the situation, has been going to therapy, and you are providing responsive, affectionate, and appropriate care to him, that he will not be scarred or warped for life by this one incident.
PS As to your friend - if you two are really tight, I would be inclined to ask her straight up if this incident is something that she is planning to sever the friendship over and if there is anything that can be done to save the relationship because she is a pretty important person to you. I would be pretty distraught if one of my closest female friends cut off contact with me without even a full conversation about the decision. Hopefully she will come around and you can work out a way to remain friends.