I've fattened up the answer in #2 to cover one of your new questions but here's the answer to the other one:
Downloading purchased content from the Apple/iTunes Store
The typical approach to media storage is big external drive. So download any of it to such a drive and organize your movies/tv shows/etc however you like. Then consider unchecking that box referenced in #2 and drag and drop the downloaded media into the TV app. That will index them without copying them to the internal drive (and eating up internal drive space).
Bonus:
possessing the media means you can sync it and/or enjoy it when you lack broadband or don't want to hog up wifi by streaming video. For example, sync a mix of purchased and your own videos from the TV app to your iDevice and then you can fly and enjoy the media, even if you have no internet connection. Possessing purchased media also means that should some behind-the-scenes action make one of "your*" videos stored in the cloud disappear, your local copy will still play. It's always better to possess what you own vs. trusting for profit strangers in some cloud to be caretaker of your* stuff.
The one "weakness" in this otherwise "whole solution" is that 4K versions of purchased movies are stream only. So while you can download up to 1080p HD versions of purchased movies, if you want to watch one that have a 4K version, you need to go back to the TV app on AppleTV for access to the 4K version. However, that's just a mental awareness thing: take note when you want to watch a purchased movie and if you want to watch it in 4K, open the TV app and locate it there. Of course your own home movies shot in 4K and/or rips from Ultra BluRay discs in 4K will play just fine via Computers app.
Another tip: you can tag your home movies as movies or even home movies and either tab will be available in Computers app on AppleTV but I have chosen to tag my home movies at
TV Shows. Why? Because TV Shows can be easily grouped by "Season" (Year) and even stacked up in date order during that year. If you have only 3 videos, this is no big deal but if you build up a big library over the years (I have HUNDREDS of home movies), it's very helpful to group them by year "at a glance." For example, which Christmas video from 10 named Christmas do I want to watch? If I know it is Christmas 2014, I can go to Season 2014 and watch the ONE video named Christmas in there. If I tagged them all as Movie, I better name them all with dates to find that one: Christmas 2014, Christmas 2015, etc. The TV Show tag simply offers a lot of handy organization options for lots of home movies, not available if they are tagged Movie or Home Movie.
Tagging your own movies can be very helpful here. Free tools like
Meta-Z and
Subler can make it easy to tag them just like professional videos... even with thumbnail images that display when browsing them. Use tools like those to present them just like purchased movies are presented: thumbnail poster, descriptions, dates, ratings, format, etc.