Yes Points are considerred Closing Costs. Regarding the second part of your question, when asking a seller to pay your closing costs you have to offer them a higher price on the home. The question then is "Who is really paying the Closing Costs?"
Paying points or not is a seperate decision you need to make. Generally for every 1% Point you pay you can expect to recieve a .25% lower rate. You can call me at 216-324-8113 if a further explaination is desired. If you are a first time buyer there are other programs that might be of interest to you. The phone call and conversation are without cost or obligation.
As an example, if you borrow $200,000, one point would be equal to $2,000. In general, paying this up front will reduce your interest rate by approximately .25%.
So to answer your question..Yes they are a closing cost. These points are generally deductible the year you close as well so keep that in mind when you are filing your taxes!! . This is true even if the seller is paying for them.
If you have any more questions I would love to help you! If you are looking for a good lender I can recommend a GREAT one. His name is Raub Warner with the State Bank. 614-571-0626 Raub's Cell. He has helped all of my buyers with their questions in financing!
That's how a seller looks at it.