To address all 3 posts in one go.
You have linked to an image in the Moodle docs that gives an overview of the checklist functionality - it shows what a checklist looks like from the student's perspective, as well as the overview that a teacher is able to see. The only thing I can guess at is that you haven't been able to reach the 'edit checklist' page (which isn't shown in the screenshot you linked to), which can be reached by clicking on the checklist and then clicking on the 'edit checklist' tab. The 'student checklist items (so that students can add their own items to keep track of)' is one of the settings for the checklist, which does exactly what it describes - could you explain what is not working about this.
The next post shows an error related to CONTEXT_CACHE_MAX_SIZE - this is not something I use in my checklist code, so the problem there is unrelated to my code.
The other warning message you have included is related to the 'mylivechat' block, again, this is nothing to do with my checklist plugin.
I still can't see anything in my checklist code that would redirect you to the 'my home' page, so I can only assume that it is some other plugin you have active (maybe the 'mylivechat' block?) that is causing the problem.