How do I enter my single member llc information into the Turbo Tax Self Employed online version? Follow up to that, how do I file a final business tax return?

A single member LLC is not required to file a separate business tax return as all your income and expenses will be reflected on your personal return on Schedule C.  

In TurboTax Self Employed, you can enter "self-employment income" in the search field at the top right of the screen.  Then select "Jump to self-employment income" and you will be brought to the section of the program to enter your single member LLC income and expenses.

Within the general information section related to your self-employment income, you can specify if the business stopped during 2017.  

What if the type of income received is partnership distributions on a K-1? Is this still considered "self employment income" of the business

The distributions are not self-employment income, but any amounts in Box 14-A are considered Self-Employment.    @Gdwilliams