@yoroshikue masturbation for both males and females work by stimulating the genitalia (penis, vagina, balls/testicles, breasts, nipples, and the anus), since the genitalia are covered in many nerve endings, and thus are sensitive to pleasure. The genitalia are sensitive because they are used for sexual reproduction, and thus need to be ('cause well, science.)
Males can be satisfied by anal sex because of both the anus being covered in nerve endings, thus being sensitive to pleasure, and because of a gland called the prostate gland that controls some sexual functions. The prostate is next to the rectum and gets stimulated by penetration when the penetrating object(s) (probably a penis in this scenario) touches near or on the prostate (through the rectal wall).
Females being satisfied by anal is a harder thing to explain. Some females can be aroused by anal, while some cannot. Some say that the G-spot (a spot inside the vagina that is particularly sensitive and thus more prone to orgasm) can be accessed from behind through means of the rectum, and that this is why females can receive pleasure/achieve orgasm through anal, although there's no hard evidence (that I'm aware of.)
Not sure what continuously have sex means, but there's something called the refectory period for males where after ejactulation/orgasm, there is a brief period where you cannot achieve full erection and/or orgasm again. This refractory period increases in length of time as you get older, as well as increase in time the more orgasms in a row you have as well (this means that the older you get the harder and harder it can get to have multiple orgasms in a row, or even just one. Although if by some means you were to in theory have a magic penis that never goes down, then eventually the penis and/or the vagina it is penetrating may potentially begin to get friction burn and it will get uncomfortable. Think about what would happen if you kept rubbing your hands together and didn't stop, something like that (although lubrication may prevent that, I can't say since I've never had continuous sex.)
No, I don't think a penis can burst from a boner, but some people may have a condition in which erections may last a long time and can begin to get painful and cause problems, but I don't know much about that. It is somewhat rare, though. If you do have an erection that lasts for more than a few hours and won't go down or gets painful, go see a doctor.
I'll answer any questions you or anyone may have.