Form 1040 is the main tax return form. It applies to nearly everyone.
Schedule 1 provides additional income-related line items for Form 1040, which are totaled and entered on Form 1040’s Lines 7a and 8a. Up until a couple of years ago, all these additional line items were included on the 1040 itself, but they decided to simplify the 1040 and breakout some of the lesser-used items to a separate schedule. You only file Schedule 1 if you have anything to enter on those lines.
Schedule C is what is used to report revenue and expenses for your business. On it, you will calculate your business income or loss. You follow the instructions to know what to do, but generally you will put your business income or loss from the bottom of Schedule C’s first page on to Schedule 1 Line 3. This gets totaled with everything else on this part of Schedule 1, and that total goes on 1040 Line 7a.
In addition to Schedules 1 and C, you need to look at Schedule SE, the schedule for self-employment tax. At the bottom of Schedule C, you’ll see that it tells you that you need to enter your business profit or loss into Schedule SE to determine how much self-employment tax you owe. If you do owe self-employment tax, you’ll also need Schedule 2.
Finally, to answer your last question: If you are filing your tax return, then it needs to be a complete return, including everything you need for your situation. If your income is low enough, you may not be required to file at all (see the 1040 instructions for details), but if you choose to file and you have a business, it needs to be accounted for with Schedule C. If you have a business loss, the loss can reduce the tax you might be paying on other income not related to the business.