How would Caine & Weiner enforce this overseas debt? My assumption is that, to do so they would need a judgement from the UK?

This has been posted in immigration, so I have redirected it to debt collection for a proper response from that forum.

Can my us citizen wife sponser me for green card while i am in pending on asylum case? We married before I filed for asylum

Your citizen wife can petition for a green card while your asylum application is pending.

Applicants with any lawful status, such as a tourist visa, student visa, or work visa, can apply and typically receive the asylum decision by mail...

The most recent tax year on form 864 means 2015 or 2014 for my case?

Year 2014 is the proper year since you have not filed 2015.

Once my spouse becomes a US citizen, should I still count her against my assets/bank accounts if I want to sponsor more people?

She remains until she becomes a citizen or qualifies with 40 quarters of work.

How many time/days/months can my mom get the green card since her marriage? How many times/days/month can I get a green card ?

Because she entered the country illegally she will have to consulate process and seek a waiver for Inadmissibility by proving extreme hardship....

What to do and what are the chances? Will both us be interviewed together? Because we have one set of the supporting documents.

No your citizenship interview and tests will be done separately.

How many times can a sponsor file his or her financial support and sponsorship for the immigrants in an year ? Multiple or only

As many times as your income/assets will allow.

My xhusband file was in NVC and I got divorced wth him Bt he never been here.after I get remarry do I need divorce papr to aply

Yes you will need to provide a certified copy of your divorce among many other documents.

Can an European citizen with American relatives apply for the green card?

Cousins may not petition for you, only parents, siblings, and spouse.