Android
In Chrome, open 578Movie, tap the menu and choose Add to Home screen, or accept the banner Chrome shows. The icon lands on the home screen, the app opens full-screen without the browser bar, and your list, your country and your episode marks are inside it. It updates itself every time it opens. Nothing to sideload, no APK to find: the app is the site, packaged for the phone.
iPhone and iPad
In Safari, open 578Movie, tap share, choose Add to Home Screen. Apple only lets Safari install web apps, so use it for this one step even if you browse elsewhere. The app shares Safari's storage, so everything you saved carries over.
What it does
The whole site, on a phone: search by title or actor, the shelves, every series with seasons and episode dates, Reached this episode, My List with export and import, a country selector 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 on every page.
Television
Any television with a browser opens the site: Android TV, Google TV, Fire TV's Silk browser, most smart TVs. Bookmark the address, search with the remote or the voice button, choose the country once, press Watch now, and the title opens in the service's TV app if it is installed, which is where it plays in HD or 4K. Or cast: open the title on the phone, press Watch now, pick the service, cast from its app, and keep My List in your hand. The television guide has each device.
Downloads
The download lives in the service you open with Watch now; most services save films and whole seasons to a phone or tablet in HD, with subtitles, for weeks. The downloads page has the details.
Two devices
My List belongs to the device it was made on. Export on the first, Import on the second; the lists merge and the later episode mark wins.