I read up on it and saw that the IRS can "charge" the loan provider on
interest even if the loan provider doesn't charge interest, but this
is normally mitigated by the 0% interest being considered a gift and
as long as it's below X amount your fine.
Yes, this sums it up. X is the amount of the gift exemption, the $14K.
However, you must differ between loan with no interest and loan with no paying back. With loan with no interest you're still giving a statutory gift of the IRS mandated minimum interest. However, the principal is expected to be repaid to you and you must show that this expectation is reasonably fulfilled. If you cannot (i.e.: you gave a "loan" with no intention of it being paid back), then the IRS will recharacterize the whole amount as the gift, and you'll be on the hook for gift tax for the amounts above the exemption.
What defines a loan vs a gift in terms of the IRS, is it simply that
the loan will be paid back, or is it only considered a loan if a
promisary note is made?
As I said - you must be able to show that the loan is indeed a loan, even if it is with no interest. I.e.: it is being repaid, it is treated as a loan by all parties, and is not an attempt to evade gift tax. Promissory note is not a must, but will definitely be helpful in showing that. But without the de-facto repayment of the loan, it will be hard to argue that it is not a gift, even if you have a promissory note. That means, you should make a loan in such a way that the borrower will (begin) repaying it reasonably soon, so that you can show payment schedule being followed and money moving back to you.
Reasonably soon is not of course defined in a statute, so do consult with a EA/CPA licensed in your state on how to structure the loan so that it will not appear as an attempt to evade the gift tax.
Are there any limits on how big a loan can be?
No, but keep in mind that even with statutory interest charges (published by the IRS monthly, see the link), with large enough loan you can exceed the gift tax exemption.
Also, keep in mind that interest is taxable income to you. Even if you gift it back (i.e.: the statutory interest).