I'm in stage 3 of development according to your calculator. My penis is 3.8 inches (9.6 cm) and my scrotum I can't measure, but is that a normal length for a 13 year old's penis? Also I have noticed that my penis, when erect, I can push it down, let go and it flings back up and hits my tummy. Thirdly, I do penis exercises to make it bigger. My penis when I am at school gets erect, why? When I am in bed, and I looking at naked girls on the web, and I get a erection, why does the skin on my penis roll back just a little bit? Lastly, I am wondering if the penis exercises are working or not, and what's the average length of a penis? What happens when you have sex to your penis? When you stick it in the vagina, do you feel anything flowing out or not? Do you think I should have sex early or not?
You won't find statistics on the average length of a penis during adolescence simply because boys are growing, their penises are changing size, and every boy starts at different times and grows at different rates. The average adult penis is about 6.5 inches (16 cm) in length, though "normal" is considered to be between 3.5 inches (9 cm) and 8 inches (20 cm). For being in stage 3, a four inch erection is very typical.
To cause an erect penis to angle upwards, there are cords near the base of the penis called the fundiform ligament and the suspensory ligament. When your penis is flaccid, the base points upwards, but the rest of the penis flops downwards. Only when the shaft is erect does the penis then point upwards.
The ligaments have some give and can stretch bit. So when you pull your erect penis downwards, you are stretching the ligaments a bit. When you let go, like rubber bands, the penis is pulled back upwards. Those ligaments eventually will get stretched permanently as you get older and your erections won't angle upwards nearly as much.
Exercises make muscles bigger. There is no muscle in your penis, so no exercise can make it bigger. Of course, people are able to fool young men, such as yourself, with such claims but that is because their penis is getting bigger anyway due to growth. The size of your penis is dependent solely on the genes you inherited from your parents.
Spontaneous erections -- erections that happen on their own for no apparent reason are a result of your brain trying to learn when erections are appropriate or needed. It will settle down by the time you get into your twenties. See: Why do boys get spontaneous erections?
Though I understand the desire to look at sexually explicit pictures, it isn't good for you. Pornography warps the way men look at women. You start seeing them as objects instead of people. That will make life more difficult for you as you get older. See: Does pornography change a person?
I assume that by "skin rolling back a little bit" you mean that you are uncircumcised. The skin at the end of your penis is called the foreskin. It is supposed to pull back completely during erections to expose the glans (the bells shaped end of the penis). If you are unable to do so without discomfort, then you have a condition called phimosis. For more information, see: I'm uncircumcised. The skin on my penis doesn't pull back all the way to release the tip of the penis. I think it should, but I don't know if I should see a doctor.
When a man has an orgasm, he can feel both the muscles clenching to cause the ejaculation as well as semen moving out the penis. It is similar to the fact that you can slightly feel the urine moving through your penis when you use the toilet. Orgasm is a very strong feeling and the feelings of the actual ejaculation are mild.
Sex belongs only in marriage. For a detailed discussion of why, see Why Sex Outside of Marriage Is Wrong.