I agree with Mr. Smith. The original I-130 is no longer valid.

Can I file for STEM if my I130 got approved? SOS

You can try. Since the I-130 won't have any value for a while, they might approve you.

I-539 delays

There is no 240 day rule for an H-4 extension. She can stay until a decision is issued.

Can my mother file I 130 from her immigrant visa stamp to petition her child of 19 years old while she is out of US?

Unfortunately, no. If you look at the visa, it states that it becomes a I-551, proof of having a greencard, only after she enters the US. ...

My citizenship interview is on April 26, I have a trip scheduled for May 14, can I travel?

ESTA is a way that people enter the US without a visa.

How do i change from J1 - my B1/b2 while in the usa

Leaving and returning to the US will be faster than filing for I-539.

Would my sister be affected due to my father's I-485 denial?

No, this shouldn't impact on her in the 12-22 years it will take before she has an interview.

Talk to an attorney, there is probably a way to have a judge sign an order correcting/amending it.

Q 1) can my dependent stay back in US for a month or two since their i-94 is valid for next 1 year? A: no Q 2) If not, can they apply for...

You don't really need to include many documents. Follow Mr. Smith's suggestion.