H4 application submitted.

As my colleagues mentioned be patient it often takes a few weeks

They will need to establish their intent to depart the US at the completion of the J visit among other eligibility requirements.

Is it possible my Mom get a green card from her green card holder boyfriend?

Your mother and her boyfriend will need to marry before he is eligible to petition for her. A a resident himself the process will take many months...

Where to send I485 and whether I-864 needed?

check https://www.uscis.gov/i-485 for where to file I-485. Also submit AR-11.

Approved I-130 in removal process

What did your attorney request when the I-130 was submitted? Are you looking to obtain status from the Immigration Judge or looking for a...

USCIS will likely not change the start date from the date requested. The card should arrive soon and you will know the start date.

Renew/Extend I94

You need to file for an extension with USCIS or depart the US and return.

Are the marriage from an american girl delete the block ?

More information is needed particularly the basis for being barred from the US.

Can I still get a J2 visa if my husband applied for TPS before that?

If your husband maintains J-1 status you may seek J-2 status.

Rent apartment and immigration. will this deny my citizenship ?

Renting a lower income apartment does not impact US citizenship eligibility.