Home Equity Loan Same As Cash?

The short answer to both your questions is "yes." In either of those scenarios, it is completely acceptable to use funds from a Home Equity Loan/Line to purchase another property; if you use it as a down payment, then the borrowed money is counted in your qualifying debt ratios, but the new loan is only based off the loan actually made against the new property's title. I'm not quite sure what you mean by "cash purchase for lower closing costs," but you certainly wouldn't have any lender, appraisal, escrow withholdings or lender's title insurance costs required to purchase the home, so yes the costs would be considerably lower on the new purchase.

You can use a Home Equity loan for anything. It is your equity and therefore your money. One caution, is a lot of bank are starting to freeze unused portions of equity lines, as values diminish. Make sure you check with the Home Equity lender to insure your funds are good and no plans to reduce the line. As for less cost, absolutely. All you will be required to pay is title fees to legally transfer your name to title. Of course, any inspection or Appraisal fees if you want those services perfromed before you buy.