Infuse Pro by FireCore
https://appsto.re/gb/xJEp1.i
This app is absolutely incredible for what it can do on iOS! Getting said files on the iPad in the first place is another question but Infuse can play anything you chuck at it and it can AirPlay said content directly to an Apple TV without converting it on the fly! Just amazing, and take it from me, it performs silky smooth on an iPad 3rd gen so anything newer will be a breeze!
As mentioned above, it can play local files (as well as from external [wireless] HDDs etc) but only from another apps open in sheet due to the lack of file system access! This app is a prime example of an app that would take excellent advantage of access to a real file system!
As for downloading files on to iOS
major pain in the ass. You can't connect a USB HDD, and as for apps which download from various online sources, well they will never get past Apples lock and key due to the closed nature of iOS. You obviously can't rip a bluray disk on to iOS using an iPad so that leaves you with.... You guessed it
ITUNES. Funny that.
This pretty much sums up iOS and it really frustrates me the fact one would have to buy an expensive laptop on top of their 95% capable iPad and lug around two devices just to fill that 5% gap where iOS fails. And a lot of this is down to how tight Apples leash is on iOS apps, how restrictive there APIs are and the fact they STILL haven't allowed users basic access to the file system with a corresponding Finder app and new 3rd party APIs.