Does the Basic plan on TurboTax not cover filing business income and expenses if I am filing myself?

Do you need to file Schedule C for self employment?  

You can enter Self Employment Income into Online Deluxe but if you have any expenses you will have to upgrade to Premium or use any of the Desktop CD/Download programs.

How to enter self employment income

https://ttlc.intuit.com/community/self-employed/help/how-do-i-report-income-from-self-employment/00/26653

Can you deduct business expenses?   If you have the desktop program (any version) - Yes.      If you have the Online version - No, you need Premium.