My marriage based i485 is pending for over a year now. I havent heard from the immigration after my interview.What's my options?

Wait 180 days or hire a lawyer to work on it. I've done this for my clients in Los Angeles.

I am in an abusive relationship with a 2 year old child. We both have dual EU/US citizenship, the father holds a green card.

I agree with my colleague.

What is my current case status?

If you properly updated your address, you should be ok. However, I would keep following up.

I am waiting for the decision on my H1B petition and got an offer to initiate L1 visa with my previous company .

Yes, you may apply for both.

You may correct your application at the interview, no problem.

Cancellation of Removal Process

I've represented many Los Angeles clients in your dad's position. I can say without a doubt that you need to hire an attorney as soon as possible.

Best course of action for a US Citizen to marry a non-US citizen who is currently in the US legally.

If you're sure you want to get married, and you didn't have the intent to get married when she came, then get married now. It's much easier.

Immigration Tourist Visa

Yes, one can apply for an extension. I've done this many times for my California clients.

I WANT TO APPLY FOR US CITIZENSHIP. I'VE HAD A GREEN CARD FOR 10 YEARS NOW. CAN I DO IT NOW OR SHOULD I WAIT?

For sure, you need to hire an immigration lawyer to sort this out. I can tell you that you may have a problem. Need to see all the records....

Please help with i864

This is way too many questions for an internet forum. Go get an attorney consultation in your area, many lawyers offer free consultations.