If a finance charge (Origination Fee, Life of Loan, Closing/Settlement Fee, etc.) is paid outside of loan closing, does the fee still effect the APR?

Finance charges impact the APR regardless of when they are paid. If they are paid before closing, then they are prepaid finance charges. If they are paid after closing, then they are added into the finance charge total.

So if someone borrows $100k and they pay all of their fees upfront (including $300 finance charge) and we select that the finance charge effects the APR it shows the "Amount Financed" as $99,700 on the CD. Most of our customers finance their fees and this looks correct, but if they pay everything upfront and want $100k available to them I am not sure how to correctly disclose this.

You put the fees in the borrower paid before closing column on the CD. Otherwise, I do not understand what you mean.

Unless you are talking about the amount financed and not the cash to close table.

If you hand me $300 and I hand you $100,000 - how much more do you have than when you started? $99,700, correct? That is amount being financed.