Let's start with the easy one:
The cramps you get with your period is your uterus contracting to separate the lining from the rest. This lining breaks up. It is full of little blood vessels. This is what forms the menstrual debris that you call your period.
When you have an orgasm, your uterus contracts in the same way, it is just much more pleasurable for you. So while you are menstruatin, these contractions will/can speed up the breakdown of the lining and push it out much quicker. This will cause the stop start effect, with the very heavy flow a bit later. Hopefully your period will be a bit shorter for all your effort.
For this reason, a good orgasm will often relieve menstrual cramping, and it can make your flow start a bit earlier if done before your period, or make it restart if done shortly after your flow stopped, or make it quicker if done during your flow. Orgasms during your flow phase of your cycle is actually quite good for you. It is thought to combat endometriosis, and it puts you in a good and relaxed mood, and help you sleep.
The first part of your question is more difficult to answer as you need to be examined to determine the exact reason.
The first time you bled was likely your hymen. Does putting a tampon in when you masturbate hard help? Does it absorb blood, or does it stop bleeding altogether. What do you use to masturbate hard with? My suspicion is that you either cause micro tears in your vaginal wall, or bruise your cervix. Make sure what you use are smooth, clean, no possibility of breaking or sharp edges, make sure you are super wet, and stay wet. And don't go too deep.
You can try to put something inside your vagina (whatever you are masturbating with), but then rubbing your clitoris until you orgasm, rather than pumping hard and fast into your vagina.
You can also take a mirror and see if the blood is coming from inside your vagina, or somewhere where you can see it.
Take care, and remember to keep everything you use clean, and very well lubricated.