How do I know if someone applied for my moms residence before ?

You can do a FOIA request to obtain a copy of the immigration file.

No it is likely not worth the time or hassle involved.

No that is not the case and you may depart without consequence.

Yes you may and the best course of action depends on your personal circumstances. Best to consult with a lawyer for guidance.

What to do next about a denial due to over aging in a family based sponsorship?

I agree with my colleague. You will need to provide the case for review to an attorney to better assist.

Can i change my status from F1 to immigrant status after I-130 is approved?

Possibly but more information is needed. Best to consult with an attorney for guidance.

Yes you may but best to have the filing receipt as proof.

I file for I-130 for my wife I am green card holder I want to know how long it’s take?

Next step is awaiting approval which will take 1 year or more.

The I918B must be completed fully and accurately so best to return with the necessary citation.

Is there faster way to bring my adult daughter in US than i30 application?If she goes to a community school?

Yes, school is an option for your daughter. Best to explore options with a consult with an attorney.