My Parents are green card holders can they sponsor me a daca recipient.

Yes they may petition for you as an unmarried son or daughter.

Receiving unemployment benefits should not impact your status.

Anything to do for finalizing i130 process?

It is best to wait up to 120 days for decision.

Hello , I wanted to ask can a illegal immigrant see a family member in a detention/jail without getting asked for papers ?

Best to contact the prison system to inquire about entry and identification requirements.

Taking unemployment will effect my citizenship or not ?

No this will not impact your application for citizenship.

No this should not impact naturalization prospects.

Can I still apply for DACA if I entered the U.S in 2009? I meet all the other requirements but this one is unclear.

Unfortunately no, not based on time of entry.

Likely not but you can contact either USCIS or NVC to inquire further.

What is the USCIS form name/number, income limit to invite my mother from overseas as a non-immigrant?

Do you want to petition for her permanent residency or have her enter as a tourist?

Both questions refer to the documents used at time of last entry.