I moved in with no lease just a contract. How long can I live on the property. I call the police on my landlord.

It is unclear what you think the difference is between a lease and a contract - a lease IS a contract (between the landlord and the tenant)

Do I need to hold the check he sends until court, and is there any recourse for his verbal abuse?

If the verbal abuse rises to the threatening level you may have a claim against him.

I am in an apartment in Capital Hill in Denver. My dishwasher has been broken for over a month and the building is infested with

Make sure you keep all proof of your communications with the landlord about the ants infestation.

WHAT SHOULD I DO? I DON'T UNDERSTAND THE LANGUAGE AND CAN I BE EVICTED AND IF SO WHEN? PLEASE I AM SO SCARED? PLEASE ADVISE ME.

Do a quick Google search to find a free legal services org. in your area.

What's the best way to get my belongings out from a hostile household?

You should be able to call your local police department and see if they will send an officer over during the moving period.

What exactly should I do?

I would just like to add that you should also go to the doctor to get proof of your illness.

How the US firms officially invites foreigners, workers, partners to the US? (docs, petition, request which org like USCIS)

How do you know that the consulate illegally denied your visa application?

You are encouraged to have a face to face consultation with an immigration attorney before departing the U.S. for long periods of time.

Do we have to register our marriage in the U.S court in order to remove the conditions on my residency?

You do not need to register the marriage in the U.S., just present a copy of the foreign marriage certificate (make sure to have it translated into...

Concurrent filing i-130 and i-485 and i-765 ( which center and filing fees)

Both attorneys have given excellent advice -good luck!