Is it legal for a court system to be closed for " the holidays " from Nov 2016-March 2016 ?

Not an immigration matter but there must be a communication problem regarding a criminal court being closed for 4 months. Suggest you speak with...

Based on your facts you may not reinstate it as you intended to not respond. There are no circumstances beyond your control you can attach to.

I'm petitioner but I don't have any income to be a sponsor. I found a joint sponsor for my wife Do I need mantion me in i864

You must actually file I864 regardless of your income. If it is insufficient as you say, a joint sponsor will need to file theirs.

Assuming you are here without status, yes, and for illegal presence as well.

Joining your husband is not a problem and you can file here and request to have your passport sent overseas.

N 400 application stuck up in name check

At this stage of events frustration can set in but there's not much you can do but be more patient as it just takes time.

Filing for my mother

Your mother can sponsor them if they are single.

Can my family (Green card holders) spend more than a year outside the US

Based on your facts you indeed have a problem with abandonment of your green card. It is obvious you have thought out your plans but they are...

Yes you should enter the current last entry and that you are still here.

Filed I-130 for my brother in India. Board of Immigration denied I-130, what should I do now?

Probably the first thing you should do is try to overcome the objection with the birth certificates. If you cannot do that the result will be the...