We are making payments to a mortgage company for our house. We built the house on property that we owned outright because we paid cash for it. WOULD the mortgage company be interested in buying the land from us?
When you obtain a mortgage loan it is based on Real Estate plus improvements. This means that when you borrow money, an appraisal is done that includes the value of the house andthe land underneath it. That doesn't mean that you borrowed all of the value of what the land/house was worth, but when you build improvements (house, garage, barn, etc) on any Real Estate, they become linked. A mortgage would have been signed by you at the time of closing that outlines exactly what is being held as collateral. In the case of the mortgage loan, the collateral used would have been the land plus improvements. This means that the loan that you have right now includes both the house, and the land that it is built on. There is no way to separate the 2 in the eyes of a lender.
One caveat to this is a 'personal property' loan, typically done on something like a mobile home. A mobile home is considered personal property because it is not tied to the Real Estate it sits on. In that case you can obtain a loan for the mobile only, which is separate from the land. If the home you built on your land is deeded as Real Estate, and chances are very good that it is, you no longer own the land free and clear, you used it as collateral along with the structure that was built on it to obtain the loan.
As for the second part of your question, mortgage lenders don't buy land, they are in the business of lending money against collateral. The collateral that they lend against are land and homes that sit on land. It may be possible to get another loan, using remaining equity in the house/land, but the bank will not buy land from you.
For an answer to this question you may want to refer to my comments on your other question. You are assuming that the lender does not have a lien on your property. You may have given your property as security for the money you borrowed to build the home. If so, why would a lender have an interest in purchasing your property? They would already have an interest in it. If you gave the property as security for the loan, you no longer own the property "free and clear." Of course, only your mortgage company can tell you if they are interested in buying your property. But I imagine that, given the current state of the economy, they own way more real estate than they would like. Which means if you are lucky, they don't want your property and may be willing to work with you to find a way for you to keep it.