Like any other filter, this one protects the front lens from water splashes. 

I have not looked for a specific travel case, but unless you are being really rough with it I would say a padded envelope or a generic small case would do it. It's pretty sturdy. I take it to to the office sometimes and just put it in one of the pockets of my laptop case. Also, for extra protection against scratches I never removed the clear plastic film that comes over the screen. Except for the red ""pull here"" tab, you can't tell it's there. 

Yes there is a case/stuff sack and as far as accessories there are two batteries, charger, and 32GB MicroSD card. Pretty sure there was a lens cloth as well. 

This Hohem gimbal stabilizer is equipped with the latest “Hohem Gimbal” APP, which can interact well with the latest iOS13 system and improve the user experience. So it's perfectly compatible with iPhone11. 

Don't know. We have an iPhone 6s and it works with that.