The current status can be visa overstay or AOS pending.

Can an illegal alien get arrested and deported while leaving the USA with a 2 way return ticket and invalid I-20?

He can likely depart the US without issue but reentry is another concern.

DDo you help with I 130 forms?

You may wish to find an attorney through the Avvo search tool for further assistance.

When do I need to change my wife's family name?

She can apply for her passport with the new name and you can provide the marriage certificate to prove the legal name change.

What is the letter of extension?

The extension letter provided proof of your extended status pending the I751 adjudication.

Can my mom go to the US using a tourist visa?

She can attempt entry with a showing of her specific basis with return itinerary, though the pending immigration petition will likely impact that.

How long should i be married befor applying for my green card?

It is advisable to consult with an attorney for such a matter as marriage upon entry on a visitor visa with subsequent AOS may be questioned.

When does USCIS check for good moral character? from conviction or last day of probation?

You should apply after your probation period has ended and you have a final adjudication on the matter.

What would be my best option to have a Venezuelan woman, who lives & works in Colombia here in the USA?

She can apply for a visitor visa if she is able to establish sufficient familial and financial ties to her home country as well as the basis for...

Can my fiance petition for K1 visa be denied?

Yes you can petition for your fiancé as you have met within the last two years. Consult with an attorney for guidance.