Yes you may include this and provide explanation if requested.

Case was received means that the application was accepted by USCIS and approved means that the I130 was actually approved.

You may apply 2 years and 9 months since date of residence if married to and residing with USC spouse.

Accidentally put my dad's second name on G-325A, will this affect my N-400?

No this should not be an issue and can be explained at time of interview.

Will my parents need to travel to the US?

They should return to the United States before the one year absence. If they do not, a returning resident visa may be an option.

Petitioner/Sponsor makes K1 wife and kids pay for everything and forces them to work illegally ?

You may be eligible for VAWA relief given the information provided. Best to seek shelter and contact an attorney for guidance.

Can I still derive citizenship thru my father when he just acknowledge me when I was 15 years old?

More information is needed about your case. Best to consult with an attorney.

What kind of a financial aid am I eligible for if I apply for universities in the United States on my L-2 visa?

Best to speak to the university directly for such an inquiry.

Can we change interview location to be in USA because we still in asylum case waiting for court?

No, adjustment of status would not be an option given the circumstances indicated.

If your previous residence were all short and temporary in nature, you can indicate your permanent address for this purpose.