Yes, our WordPress Speed Optimization for Non-Profits is completely free. We generally ask for "View" access to your Google Analytics account so that we can track if the improvements that we've made as it relates to your traffic. But this isn't a requirement, and you can remove access anytime.
We will let you know if we find something during the WordPress Optimization that we think you should address on the site. We'd be happy to help you with these things, but we aren't trying to sell services.
At the minimum, we will need Admin Access to your WordPress install. We request access to FTP and your Web Hosting Admin, but that isn't required. Typically, we recommend setting up us as separate users for your site, we can guide you through this process if needed. We can also provide instructions on how to share login credentials securely.
WordPress is the most common Content Management on the planet and is very common in the non-profit community. We are looking at how to expand this offer to other platforms, but unfortunately, they are far less predictable in the amount of effort that it requires to get good results.