Having been around inflatable pools on and off throughout my life, I'll chime in with some input.
Stop.
You say you are going to put this on your patio? Is the patio in anyway rough, especially the brushed/broomed concrete?
If it is in anyway rough, you run the risk of ruining the bottom of the pool. I have seen it happen a lovely concrete patio was a temping setup, then a bunch of adults walking on the bottom basically abraded the bottom against the rough concrete to the point of leaking in multiple locations. I do not know if a ground sheet is the right solution there; the owners of that pool used play said as a base over the concrete in the following years (I believe they replaced the pool rather than try to repair it of perhaps they tried and it was too many patches).
Now questions.
1) Ground sheet: I've seen it done both ways. A ground sheet is probably best practice, but plenty of pools have held up for years being placed on area in the yard that has had all sharp items (rocks, acorns, cacti, pine cones, and on and on) removed). So I would say if you carefully prepare the site it isn't needed.
2) Chemicals: unless you are setting the pool up for a very short period of time, yes you will need to treat the pool to keep bacteria growth down. It is best to start before it looks like it needs it, but a few days to a week probably won't be too bad. (Most people I've known have just used the floating style and kept if supplied).
3) Cover: It kind of depends on the conditions and threats. As stated above, it might help keep wildlife out (or prevent them from discovering it in the first place). It will also keep dust, pollen, leaves, and the like out. This will definitely reduce the amount of work you have to put in to clean the pool and might let the filters last longer. Still, in a pinch you can setup without it and if needed add it later.