Normally it takes around 1 second to extract the downloading url for videos like Youtube, for some videos it make take longer, but no more than 5 seconds. If the extracting process takes more than 5 seconds, you better check the settings of your browser, sometimes it is due to the extension like "uBlock Origin". The speed will be greatly enhanced after disabling such extensions. Otherwise, just clear the cookies of the browser, the problem will be solved most of the times.
That said, with Android it is possible to install apps without going through Google. The latest is InsTube – Free Video and Music Downloader just for Android—you can only get it at InsTube's site. You download the APK (Android application package) file to sideload on an Android device. Find it in your device's downloads and click it to install. (You may have to go into your security settings and enable "Unknown sources.") There is a similar side-load app from YTD.
The same as you do to download any other videos. You just need to choose the 1080p or 4k format in the video result section, sometimes it is in the "video only" section that without sound, then you have to download the audio file (M4A) in the same result section, then you can load the video file and audio files together on your computer using the video playing software, such as VLC. You also can combine the video and audio files by using ffmpeg. Some youtube video does not have HD format originally, in such case, you definitely can not download any HD format video.
One clear example of where this works is with YouTube videos. Downloading videos from YouTube is a popular request and there are lots of tools that can do it (many that charge), so you might be surprised to learn that you can download any video from YouTube with nothing more than a browser hack. You can also download entire YouTube playlists at once.