You can apply. Remember that the arrest record will be requested along with the disposition. They need to be certified copies. I would run them by an attorney experienced in removal proceedings and criminal issues in immigration.
Make sure you have certified copies of your arrest and disposition. You will need them in regards to future immigration applications. Immigration will not see expunging as an attempt to conceal the arrest and conviction as long as you always check "yes"to the questions of whether you have been arrested or convicted for an offense. Good Luck.
You need to reopen your case and get the copies. If you were convicted or adjudication was withed you need to talk to an immigration attorney as soon as possible. The Government uses those same certified copies to sustain any charges in removal (deportation) proceedings.
Petty theft falls under the petty offence exception of the INA as long as: sentence for the crime may not be more than 1 year and incarceration may not be more than six months. Your attorney (not you) needs to look at the statute under which you were convicted to determine your situation. Do NOT travel without talking to a lawyer.
You have to say yes regarding the arrest. I know you were told that with the expungement you did not have to. This is an exception. Get the original arrest and disposition and file it with your application. I woul hire a lawyer.
You should be fine. The only way to find out with certainty is to obtain a copy of your file from Customs and Border Protection. Have all the documents you mentioned with you in case the officer asks for them. Good luck.
It depends. If he is coming with a Visa Waiver he may have an issue as to adjusting since there is a bar for becoming a resident if you enter the US in that fashion. There is an exception for those petitioned by an US immidiate relative. If he comes with a tourist visa it would be an issue of intent. As far the Cuban national there is an argument to be made that the person is adjusting under the CAA and is not subject to the bar. Nonetheless be aware that you may be detained without bond...
Adjudication Withheld is a conviction for immigration purposes. As for your specific case you should not have any issues, but you should gather all arrest reports and dispositions and visit an immigration attorney to review them alongside your immigration documents. This last information is missing in your question and is very important - what is your status in the U.S.
Your mother needs to reopen her case. The first thing you need to do is petition for her. Then after the petition is approved you need to ask DHS to join in reopening your mother's case. You should hire an attorney experienced in these matters. Good Luck.