Hello,
There are two issues here:
1. You can safely disable exchange rates if you uncheck all the checkboxes under Wallets → Exchange rates → Exchange rates providers. The only drawback is that fiat amounts will not be displayed on the frontend, and payment gateways such as the WooCommerce payment gateway extension and Events Manager payment gateway extension will not work. Disabling exchange rates will not affect operation of the ShapeShift extension. But again, fiat amounts will not be shown in the ShapeShift extension’s UI.
2. The free plan for fixer.io gives you 1000 API calls per month. The plugin pulls data from fixer once per hour. For a 30 day month this comes out to be 30×24, or 720 calls per month. The plugin will do these calls whether the site is being used or not, as long as it is online. So you see that you should not exceed the limit, if you are using the plugin only on one site. You can always check your fixer account to see how much of the limit you have been using. Simply login to the service and go to your dashboard to check: https://fixer.io/dashboard
If you are using the same API key with multiple sites then you might have to consider upgrading to another plan. If not, then there should be no problem.
Hope this is clear. Let me know if you have more questions.