I had similar problems on my iPhone 7 when I upgraded to iOS 11. This included apps totally freezing, sometimes for what felt like a minute, with very laggy input, as well as other issues, like not displaying the playing podcast controls for Overcast on the lock screen or in control center. Yesterday I did a fresh install of iOS 11 and then restored from a backup and my problems seem to have gone away. At least for me, it seems like there may have been something wrong with the over-the-air upgrade process. Perhaps this will help you.

Hmm, that means redownloading 50 GB of photos, but I guess I could try it. Do you know if you could force download all the iCloud Photos library instead of having it load on demand? Even with Settings -> Photos -> Download and Keep Originals it seems old photos (from before the device was installed) are only downloaded on-demand. I want them all offline.

I'm having this problem on both my iPad (which is newer than my phone) and with my laptops. Old pictures are not there unless I view then, although new pictures seem to be pushed to all my devices. And even if I view then, they are downloaded only at medium quality, unless I view them for more than 1.5 seconds or I zoom into them. This means I can't even scroll quickly through them, as this won't get me the original quality I want.

I don't take a ton of photos, so I don't know the answer to your question. Sorry :(

Don't choose "optimise storage" and it will try to keep all photos locally.

It will try to keep new photos photos locally, but it doesn't seem to be downloading old pictures unless I zoom into them.

Same here. On 6S animations lags very often, on iPad Pro 10.5 swiping window to multitasking causes dropping frames.

Try 'reset networking settings', this fixed it for me. Appears to be related to mediaserverd crashes (check Privacy->Analytics if that is the case on your 6S as well).

Similar experiences with tvOS 11 on the non-4k model.