How should I write the sound of crying in English scripts? Are there ...
... any differences between man's and woman's crying? Is this related to age of someone who cries and also the reasons of his/her crying?
Thank You

Question

Answer

It's a tricky thing to do - use something as cliched as "boo hoo hoo", or try to write the sound, like "uh huuh huuh"? (My example could also be read as laughter).

Perhaps it's better to follow meow's suggestion and describe how the dialogue is presented:

"I'm sorry!" he said, crying.
"I'm sorry!" he cried tearfully.
"I'm sorry!" he sobbed.

Answer

no, I do not think so )
IMHO you may try something like "aaaaaaaaaaaaa!" or "eeeeeeee!"
or it will be better to use remarks such as [crying], [sob sob], etc.