Can I apply for immigration status as both of my children are USA citizens?

Once the 13 year old turns 21.

My employer keeps telling me that they are waiting on H1B prevailing wage determination for about 2 months now

Wait a bit longer and keep communicating with your employer and his/her immigration attorney. There may have been delays due to the recent...

Do I need an attorney to keep a clean record?

Should you get a lawyer? Well yes, of course. An immigration lawyer in addition to the criminal attorney, at that. Good luck!

Can he be deported?

From the little info you provide, it sounds as if yes, he could get deported, and yes, it is also possible that the attorney can get the case...

I got my asylum approved on June 2013 and now I am thinking of getting married to my girlfriend who is currently in f1 status.

Congratulations on getting your asylum approved. An approved asylum is not sufficient standing to sponsor a (future) spouse for legal immigration...

Can my mother or any other siblings sponsor my new wife? I currently unemployed and married overseas.

If your question is whether you can have your family members be joint sponsors, the answer is yes if they are willing.

If you last more than 6 months outside the u.s. it will be a problem to become citizen why.

It is the last few years that are looked at, rather than your distant (I'm assuming) childhood to show continuous residence. The idea is that you...

Temporary working visa

You seem like a very educated person and therefore I am sure very valuable to many companies as a potential employee. Get an immigration attorney...

I agree with my colleagues. And yes, start collecting evidence of your relationship already now, you will soon need it. Good luck!

How can i submit for an adjustment of status through an IJ while I'm in removal proceeding? do i have to pay for fees again?

Get an immigration attorney to assist.