As a practical matter, the NYS Secretary of State won't or shouldn't allow that. If it somehow happens, you could claim that the ex-partner is violating the rules of fair competition, which is actionable. If you were successful in court, you would ask a judge to prevent the ex-partner from using the same name.
Yes and yes. A confession of judgment is signed before or during litigation to short circuit the litigation route. For the most part, it allows the holder to enter judgment against the other party without litigating the issue because the defendant/confessor concedes the debt due.
I would add to the others' answer that it depends. A retainer is refundable if unused, but there can be an agreement between attorney and client that provides for a flat fee that is earned upon the work done, and not refundable.
The others' answers are all good. There was a recent case on collecting the appreciated value of a collectible car that was destroyed in an accident. You can find it at http://www.thesilberlawfirm.com/2011/11/owner-of-valuable-sports-car-r.html
Assuming there is no bond posted by the owners, you should be able to continue to take over the property. If they win on appeal, the bank would be obligated to address their loss. As far as the eviction, it is possible that a judge will take that into account.
There is too much information missing in your question, but the short answer is yes, a company and its officers/shareholders can sometimes be sued, depending on the timing and claims, by another shareholder or by the company itself.
As a shareholder, you normally have an absolute right to see the company's books and records. Without knowing more details, its hard to give you better guidance, but a written demand upon the company may be your first step.