I'm from South of Vietnam and recently came to Ha Noi for the first time on a trip.

South of Vietnam would suggest that you are from a country to the south of Vietnam, but I think you mean you are in the southern part of Vietnam, yes?

While I was standing on the sidewalk waiting to buy some stuff, a lady walked by and said:, "I need your help for a moment." and then kept going.

English has spellings that make no sense at all. "by" is a word, but "buy" is correct here.

quotations usually begin with commas

I thought she really needed my help with something, wondering:, "wWhat did she need help with?".

ending punctuation in quotes has weird rules too

since this is the end of the sentence, the question mark can stay in the quotation marks and nothing else is needed

But finally, it turned out that "need your help" here actually just meant: "excuse me!

phrases or word meanings don't need colons or commas

Please correct any grammar and phrasesing mistakes!

more natural to refer to "grammar and phrasing mistakes" as in "mistakes in grammar" and "mistakes in phrasing"

this also keeps symmetry with two singular nouns instead of one singular and one plural noun

I'm from the South of Vietnam and recently came to Ha Noi for the first time on a trip.

Saying just "South of Vietnam" makes it sound like you are from another country south of Vietnam

I thought she really needed my help with something, and I wondering:ed "what did she need help with?".

Past tense

I'm from the South of Vietnam and recently camewent to Ha Noi for the first time on a trip.

"came" implies that you are still in Hanoi. "went" is better if you were going for a trip (that has ended).

While I was standing on the sidewalk waiting to buy some stuff, a lady walked by and said:, "I need your help for a moment", and then kept going.

"buy" is the verb for purchasing something. A comma is more common when introducing a quote instead of a colon. Colons are mainly used for quoting big blocks of text in academic papers.