To save Youtube videos on iPhone you will need to follow these steps:
Download an app called "Documents by Readdle" as it will allow you to save the video and transfer it to the Gallery.
After installation, click "Open" and then click on the navigator (the small compass icon in the lower right corner). A browser will open, in which you need to enter the link ytb.rip and click "Go".
Paste the URL of the YT video you want to save in mp4 into the corresponding field at the top of the page. Select "Download", and then choose the desired video format.