Hello, I'm working on the Freelance section. I have parts that I bought and sold them directly to customers at cost. Do these go in the "Supplies Expenses" section?

You can use the Supplies expense for those parts you re-sold.    If you are a small business taxpayer, you can choose not to keep an inventory.  You qualify as a small business taxpayer if you (a) have average annual gross receipts of $27 million or less for the 3 prior tax years, and (b) are not a tax shelter (as defined in section 448(d)(3)).