in Egyptian Arabic,we use لازم more than ضروري,so if you would like to say "I must" it's better to use لازم
ex:
أنا لازم اروح المدرسة
I must go to school
necessary=ضروري
like when you say in English "that's necessary"=ده ضروري
the difference between ممكن and يمكن:
ممكن=possible/can I...?/might.it's used in many situations,like:requesting permission,allowing (someone to do something),and to say that something will happen but you aren't sure.
ex:
ممكن اروح هناك؟
can I go there ?
answer:ممكن
yes,you can
هو ممكن ينجح في الامتحان
he might pass the test
يمكن also used when you are not sure
يمكن أحضر الحفلة
(I) may attend the party.
I hope it's easy:)