The rate used at bank owned and operated ATMs the world round is set by the network that the ATM uses to contact your bank for authorization of the transaction. That would be either Visa or MasterCard (or one of their wholly owned subsidiaries like Plus for Visa and Maestro for MasterCard, I'm leaving out AmEx and Discover because those are almost never involved while in Europe at an ATM). It is close to the rate you get when you Google that currency (1 EUR in USD). It can vary throughout the day, but is always the best rate available at that point in time. Avoid Dynamic Currency Conversion (an offer to bill you in your home currency at the ATM instead of the local currency) as there is no guarantee about the rate. The Wall Street Journal is out of date the moment it is printed, but can provide a guideline that might be helpful for historical purposes.
If the rate is $1.16, that is the rate you get at the ATM. The fees charged by Wells, or any other bank, are completely separate from the amount charged to your account for the currency you get from the ATM and should not be considered as part of the exchange rate. They will appear as separate line items per transaction on your statement. Wells charges you $5 per withdrawal. They probably also charge you a currency conversion fee of up to 5%. This conversion fee may also include the 1% charged to the bank by the network for foreign conversion.
There are other options that charge zero fees for foreign withdrawals. There are also many many credit cards available that charge zero fees for foreign purchases. You pay what the rate is and you are done. If you will be making multiple trips out of the country, you might want to look into getting those just for use when traveling to save the fees.
Unless you have a Chip & PIN card the PIN is not needed for purchases made through a live person. A PIN might be required at some unmanned kiosks, like train ticket machines. It won't hurt to ask your credit card issuer for the PIN. They will tell you the PIN is only for cash advances at ATMs, but they lie. While that is the only use for a PIN on most US issued credit cards while in the US, in Europe things are different. You will never be charged as a cash advance for any normal purchase you make in Europe if you enter your PIN.
Edit: It is a good idea to have 2 debit and 2 credit cards each of these 4 from different banks with you in case one gets lost, stolen, swallowed, or whatever. You are not always able to find a friendly banker willing to return your card. So keep your Wells card as a backup and use the no fee card you get from Capital One 360 or other similar bank as your primary source of funds.