1. Yes, it can help you negotiate when the seller wants to sell more quickly. The seller does not need to wait on the buyer's mortgage process. On the other hand, if the home has been on the market for very long the seller may not care if it's a cash deal or mortgage deal. Your position of strength is in the fact you are the potential buyer and the seller wants to sell.
2. SB's article is helpful but there is no simple answer: http://assetbuilder.com/blogs/scott_burns/archive/2005/05/03/Pay-Off-Mortgage-or-Invest_2C00_-Reexamined.aspx
3. If you have never owned a home, there are "hidden" costs: taxes, repairs, landscape maintenance, and remodeling.
4. If your savings are in the bank, earning minimal interest, you may be financially better off to to spend the cash on a modest home.
5. Suggestion: use a realtor, pay an engineer to check the property for major flaws, and use a lawyer.
6. Remember: location, location, location.