Re: Setting homework online and monitoring its progress.
How about Socrative? I haven't used in in a few years, but as I recall it had some games based on user-created quizzes. Various options for polling, too.
Have you looked at a LMS (Learning Management System) such as Canvas, Moodle, or Blackboard? I've never used Moodle, but I know Blackboard and Canvas have free versions. (Actually,I guess Moodle is open source, but requires you to provide the hosting). They're a bit more involved, but allow you to create full classes on them. They're widely used (at least in the US) across not only the K-12 system, but also in universities and colleges, which might give you a better sense of just how serious an educational tool they can be. You can easily integrate external apps such as Google Drive, Microsoft Office, Youtube, and a wide variety of others, although some of that functionality might be limited in the free versions, I'm not sure.
They don't have much of a 'gaming' element to them, but they have a wide variety of options for quizzes - multiple choice, essay, t/f, fill in the black, etc. You can also embed documents and video. Students can upload audio and video as well as part of an assignment. For example I frequently give students an assignment to record themselves talking in English, and then they have to upload that file. There are options to set assignments for points, or simply complete/incomplete if you're not worried about an actual grade.
They all have built-in grade books and attendance logs which make it pretty easy to not only track progress, but missing or late assignments. You can prepare elements (instructional pages, quizzes, etc.) ahead of time and either manually turn them on or set them to automatically appear (or disappear) at designated times. You can arrange things in modules if you like, and assign quizzes or assignments to the entire group, or only certain individuals as you wish.
Canvas (and perhaps the others) has a highly functional mobile app that makes it easy for students to access and complete assignments without necessarily having to be tied down in front of a computer - something my student athletes really appreciate when they're absent from class for sanctioned school events. They just log into their accounts, and can read any information I've posted, as well as download files or complete assigned quizzes, etc.
The drawback to these LMS options are that they aren't really interactive in the since of 'edutainment', but you might be able to find add-ons or plugins for them to do that. I'm not sure and haven't explored that path.
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