If I refund a ticket online do I get an email about it? Sorry, it's my first time doing this and the website said I'd get a travel voucher and the lady on the 1-800 number said a credit card refund, but it's been about a week and I've heard absolutely nothing.

Sometimes yes, sometimes no (IME, more often no). It usually takes a few weeks for them to process the refund; but they are pretty reliable about doing it eventually.

Why not just periodically monitor your credit card on-line?

Why kind of ticket did you cancel? If it was a non-refundable ticket you will likely have a credit and not a refund. UA does not send "vouchers" for canceled tickets, the value is associated with the original ticket number. When you want to use it you either go on-line and change the original reservation or call and reference the original ticket number. What did the agent say the current status of the ticket it? I believe it's pretty clear if it's been refunded, pending refund, or if it's been canceled and is available for future use.

I downgraded fare classes through a flight change.

Was it a refundable ticket? If not, you will not get a refund but rather can use the remaining value for a future flight.

If it's a refundable ticket you can get the remaining value back to your orgional form of payment.