Please correct my mistake

I was reading the Dear Abby letters; I HAVE always read it them and found that they have It given me an insight into the culture of others,  and the certain problems of other people. I was astonished with by the big great/significant/noticeable difference in culture and customs of the person who wrote the letter to that of my own (you mentioned a difference which would imply a comparison of cultures, hence you need to state the comparative i.e. what culture are you comparing it to?).
She was a Mom mother who had just become a grandmother for the first time , and she was asking whether it is might be okey okay for her to visit her daughter , or whether she should she just wait for the daughter to invites invite her (or you could say "... wait until her daughter invites her").
It is just so weird (correct, or you could say "very strange") to me because in my culture the mother always have has the right to show up in at her daughter' house home anytime and it wont wouldn't/would not be a problem .
And when the mother become a the grandmother for the first time she will would be the second person to see the baby, even before his its father get got (or "had") the chance to see him (because fathers are not allowed inside the labour room) . Then the new born baby and his its mother would spend two to three weeks in at the grandmother' house home.

Otherwise, very good English. 

Please correct my mistakes.

I was reading the Dear Abby (Always italicize the titles of books, magazines, newspapers, academic journals, films, tv shows, long poems, plays, operas, musical albums, artwork, websites, etc.) letters . I always read it them (since you used "letters" you are implying that you read more than one. Use "them" instead of "it" in this case). It gives me an insight into the culture ,  (you do not need a comma here. It should read: "It gives me insight into the culture and the problems of other people.")and the problems of other people. I was astonished with the big difference of the culture and custom of the person who wrote the letter.
She was a M mom (while mom is a title, you do not need to capitalize it) who had just become a G grandmother (same goes for grandmother) for the first time ,  (no comma here) and she was asking whether it is okey (was okay) for her to visit her daughter, or should she just wait for the daughter to invites her?
It is just so weird to me because in my culture the mother always have (has) the right to show up in her daughter's house at anytime, (comma here) and it wont (wouldn't) be a P problem (lowercase "p". "Problem" is not a person or a place).
And Also, in my culture, when the mother become a G grandmother for the first time, she will be (is) the second person to see the baby,  even before his (the) father get (has) the chance to see him (because father's are not allowed inside the labour room). Then, the newborn (newborn is one word, not two) baby and his (its, use this, unless you specify the gender. You did not for this article, so use "its".) mother spend two to three weeks in the grandmother's house .