"Question: Can I sell the house to a family member for $100,000 and avoid taxes? Does a gift tax apply for the difference between the FMV and the sale price?"
Don't confuse a sale for tax purposes with the legal definition of a sale of real estate.
You can transfer the house for a $1 if you wish. But you will need to file a gift tax return for the difference between the FMV and the sale price. Depending who whe relative is you might need to pay the "Generation SKipping Tax" too.
You will also have state gift tax implications for the state you live in.
When you report the sale on your tax return, you may need to file a return for both the state you live in and the state where the house is located.
Possibly you could post more information about WHY you need to do this or what your goals are, and the posters can give you better advice.