Refinance with no closing costs?
Any legitimate mortgage professional should be able to estimate your closing costs for you in about 5 minutes based on you answering a few questions for them. There are, in some cases, "no closing cost" loans, however, they will always carry a higher interest rate than you would otherwise...

If we are in a 10/1 arm and we have five years left on the loan.
There is no easy answer here. HARP isn't a bad idea, but the loan has to make sense. How much money is your new loan saving you? How much money are you putting back into your loan in the form of an appraisal and new closing costs? How many months or years would it take you just to break even based on those...

how soon after short sale can I purchase a new home?
Fernando is correct with his answer. If you follow the guidelines he laid out (no late payments thru sale, 640+ credit score, etc.), you could be able to buy now.

I have recently gone through a chapter 7 bankruptcy. I have a good job that pays me $80,000 per year plus bonuses. What are my chances of getiing a decent mrtage rate?
To be approved for a mortgage of any kind, you'd have to be at least 2 years out of BK-7. At that point, FHA would be your best option. If you are less than 2 years out of BK, there are no mortgage programs out there anymore, unfortunately. If you have any follow-up questions, feel free to ask. Thanks, and...

What happens on a mortgage to Co-borrower verses Primary in the event of death of Primary
In most cases, the co-borrowers on a mortgage each share the burden of the debt equally. Even if one person's credit and/or income was primarily used to secure the loan, there is no real primary borrower and co-borrower on the majority of joint mortgages.Every mortgage will have note and deed...