If you have a Freddie Mac you can only increase your loan amount by 3% or $4,000, whichever is less, (in your case this will be 3%) Any closing costs above and beyond that you will need to pay out of pocket. Odds are anything above that is going to be establishment of your escrow account for taxes which really is not closing cost and you should have money in your current escrow which will be refunded or credited towards your loan payoff.
If you were renting it and plan on renting it again than it is an investment property. A 2nd home is exactly that a home you use for your personal pleasure as a 2nd home.
HARP loans are non income qualifying so it doesn't matter how much income you make, but you do have to have a source of income. If the current loan is just in your name you just need to show your income and I would suggest you do not add your spouse, no reason to add him to the mortgage where you are upside down in the property.
When the property was rented how much money were you losing monthly?
If you refinance how much money will you be losing monthly?
Whether you should refinance or short sale is really only a question you can answer based upon your goals, your financial means and such.