I have instant apps, too and I didn't install that. Fortunately you will notice that you don't actually have instant apps installed. A quick search reveals that's something that Google instituted where you can actually open play store apps without installing them ... if you want to. I would guess that a play store update in the past added that to your library, but doesn't install unless you want it. I don't think I'd worry about it, although it does cause confusion.
About your activity ... that, too can show a lot of activity when you think you aren't using your phone, but as long as it's on, there will be various activity when your phone syncs or connects to services, and sometimes the logs can be a bit cryptic. For example, I just looked at my activity and there was an item at 3:20 a.m. when I was fast asleep. Reading the details it makes it sound like there were things going on but most likely what happened is that an app synced some data, wanted to put up a notification, but didn't have permission to do so.
I don't want to be dismissive about your concerns, but a lot of this is just normal operation of Android. It might be best if we loot at these things specifically. Are there any activities that give you greater concern?
