I have an LLC, with it's own EIN. But I am the 100% owner of that LLC. Do I need to file separate taxes for the LLC, or can I file with my personal taxes as a schedule C?

If this is a single member LLC, as I assume it is, then you just file this on a Schedule C since the LLC is deemed a disregarded entity for federal income tax purposes.

If you do not have any employees, you should not be using a separate EIN for the LLC.  You should be using your SS#.

See the attached IRS commentary on this under taxpayer identification number:

https://www.irs.gov/Businesses/Small-Businesses-&-Self-Employed/Single-Member-Limited-Liability-Comp...

If my customer gives me 1099-m with my LLC tax ID, How do I report my income?

Schedule C income and u can show expenses against it