I'll tell you what I know.
Once a sperm is in the egg, division starts. Therefore it becomes two cells.
A good way to think of identical twins is this (probably not quite scientifically correct but it gets the idea across) so the first divison has happened, but then then 2cell "forgets" where it was and starts over, thus each of the 2 cells starts at the beginning hence identical twins.
Other ways to get twins are
2 sperm into 1 egg
2 sperm into 2 eggs
these however will not be identical and may even be boy/girl instead of boy/boy girl/girl.
Can't really advise on multiple pregnancies however try google.
Given how cells divide into 2 triplets (and other odd numbers) pose a possible question - were they 4 (or even number above) and one got re-absorbed?