It comes with the top, yes. It holds temperature pretty well too.
The art on mine got damaged - I put it in the dishwasher a few times, it can be that, or the one time when I was carrying it in the same bag as a pestle&mortar and maybe it got a bit damaged there.
A small Part of the picture (size of a nail) came off. I kind of glued it back on 
It still works, mine is the plasma one… I had some lymphatic system issues recently and using the cup helped a lot (on the short term I always felt more discomfort in the hours after using it, without connecting the dots… but then once I realized I doubled down and then after a 2-3 days it got much better).
So I would definitely recommend getting the cup(s) if someone is on the verge.
Now I’m thinking of ordering one more and keep one at home, one in the office.
Few minutes only in my experience.
However, I don’t worry too much about it, I just make sure it’s generally filled. So once I finish drinking it, I refill it. Sometimes it sits overnight or while I’m at work. If maybe it sits too long, I use it for my plants 
