What are the chances of my visa being denied/me being refused entry at the border with a withdrawn charge on record?

You will not know unless you actually apply.

If I plan to work here illegally and overstayed. What are the chances that the immigration will catch me & deport me?

Your chances of being caught depend entirely on events yet to come. The best plan is to leave on time.

When is it okay to apply for citizenship after a DUI?

You will need five years with a clean criminal record before you can apply for citizenship unless you got your residency based on marriage to a US...

Based on the job desc & my educational evaluation, do I qualify for EB-2? Will the mention of MS in the job desc cause problem?

Your employer's attorney should answer this question for you.

H4 EAD request processing centres

This is a completely normal occurrence.

So can I do it ?

No you cannot proceed with the DS-260. You will need another way to become a resident. This will depend on facts you have not presented. Perhaps...

That all depends on whether you meet the requirements for the O visa. Talk with an attorney.

Can I accompany my spouse in mexico while they obtain their adjustment of status?

Yes you can certainly accompany your spouse to Mexico. However, whether it is a good idea depends on the explanation that was provided for the...

Incase of retroactive withdrawal of semester (ie withdrawal of a sem after the sem is over),is reinstatement of F1 visa needed?

The designated school official for immigration matters at your daughter's school is the person to discuss this situation with.

What is the next step? How long will it take to get my green card? Can I travel with this situation? (My son is very sick:((( )

You can only travel with an approved I-131. If you travel without the advance parole your application for adjustment may be considered abandoned. ...