Is it mandatory to get married at bridge if my partner is Mexican and I a US Citizen?

You can get married anywhere that you can both legally meet in to do so, including Mexico.

Can I take an illegal immigrant to court for child support ?

You should contact a family law attorney in your state for more guidance.

Can my fiance come to the US on his visitor visa?

He can attempt to enter and can be okay if he provides the exact reason for his visit with return tickets and itinerary.

Do i have to do anything if i have applied for I-485/I-130 concurrently (Wife is US Citizen) and visa is about to expire?

No you can wait until you receive the receipt for filing or you can check to see if your check was deposited by USCIS and expect your receipt soon...

Hi, I would like to take my sister to USA, how long does she need to wait for a visa? She’s from Moldova, Eastern Europe

You can refer to the Visa Bulletin for exact information but generally sibling based petitions take between 12-14 years.

Do I still need to submit my I-864 as a petitioning sponsor even I have a joint sponsor?

Yes you as the immigrant sponsor still need to provide your completed I864 with all supporting documents in addition to your cosignors.

If your adjustment of status was denied, any work permit is also void subsequent to the denial.

I need information from a s,s, lawyer,

It is best to consult with an attorney given the information you have provided.

Name & Surname mismatch between US visa & passport. Both passport & US visa are valid

It is best to have an attorney review, as I agree all documents should be consistent.

Editing occupation list in form DS 260?

You can notify the interviewing officer at the time of interview of any corrections that need to be made in regards to your employment.