Android
Open 7StarHD in Chrome, tap the menu and choose Add to Home screen, or accept the banner Chrome shows. The green icon lands on the home screen and the app opens full-screen without the browser bar, with your list, your country and your episode marks inside. It updates itself every time it opens. Nothing to sideload and no APK to find: the app is the site, packaged for the phone, and it works on any Android from the last several years.
iPhone and iPad
In Safari, tap share and choose Add to Home Screen. Safari is the only browser Apple lets install web apps, so use it for this step. The app and Safari share storage, so your list carries over.
What the app does
The whole site on a phone: search in any script, the language shelves, every web series with seasons and episode dates, Reached this episode, My List with export and import, the country menu on every title page, and Watch now, which opens the service's own app when it is installed. Two posters across, the menu behind the ≡ button, the search field one tap away.
Television
Any television with a browser opens the site; bookmark it, search with the remote or the voice button, set the country once, and Watch now opens the title in the service's TV app. Or cast: title on the phone, Watch now, pick the service, cast from its app, keep My List in your hand. The television guide covers Fire TV Stick, Android TV, Chromecast and consoles.
Data on the app
The app itself uses almost nothing; the film uses data on the service you open, at the tier you choose there. The file sizes page has the numbers, and 480p on mobile data is the setting most people want.