Tip: ask Google similar to will usually yield answers that will point you in the right direction. Then you can poll people for hands-on experience on specific tools.
I was giving you alternatives of platform, a direct google of "alternative to quizizz" . You can get an idea of wich ones can serve for team practice, individual practice, and then you can ask users of the specific platform you are interested in to asess their pros and cons, as usually all of theses platforms are suitable for both team and individual practice, and have a free test mode at least. In terms of LMS you must be familiar with Moodle as the most installed Open source free platform, wich facilitates the inclusion of add-ons that can provide team and individual practice, and it's competitors in the open source, freemium, free-for-educator of paid markets, but it seemed to me that what you where looking for is a web-based service for individual teachers to create practices for his students, which i'm afraid are very limited if you intend to use the free service only.