Why this security Check is taking too long ? And what I can do more than that ? should I worry ?

You can file a Writ of Mandamus - a lawsuit against the USCIS - in Federal Court. You may be entitled to attorney fees and costs if you prevail.

After 30 plus years in the US under my late wife's J-1 visa, how can I adjust my immigration status before retirement?

Do you have an immediate relative who can sponsor you? In your case grown children?

Will I be considered financially responsible for helping pay those back taxes?

No. The FA does not include responsibility for unpaid taxes.

Do I have any chances to become a permanent resident US by my wife who is the permanent resident if I am out of status?

Assuming your asylum is granted you may adjust after one year. You may adjust through your wife while she is an LPR however you would have leave...

Would it a problem if my wife, and I are her financial sponsors?

You and your wife are free to be her sponsors and there is no problem.

Can you tell me what should I do or what you recommend?

A law Enforcement Officer must have probable cause to pull you over. If an officer has P C he can pull you over.

The fact that I overstayed will affect on the process of both ideas? Which one is the best option for us?

Depending on how long you overstayed you may need a waiver to re enter the US. The waiver requires an immediate relative USC or LPR who will suffer...

I am looking at what year I supposed to apply for citizenship?

You may apply for NATZ 5 years after 1/26/2014. If you believe this is a mistake you can request it be amended to reflect the July date. You will...

Once the I-130 is approved you can file for the K visa. When the immigrating spouse is not in the USA you do not file the I-485. The immigrant...

It depends on the terms of your probation. I suggest you ask your probation officer. Also, a conviction for petty possession is a drug conviction...