Morning Ian.
The service i work for, the staff are producing a number of videos that include themselves completing various challenges (Toilet roll challenge etc) where we post across various platforms - Facebook, TikTok. Twitter. Instagram.
So firstly, as you have said, permission is required. In our case, all staff have given consent for videos to be posted across multiple platforms.
Im not sure what the copyright requirements are for using anything already on youtube. Im sure youtube would have a policy for that, or you could maybe contact the person through their username on youtube for example, and ask directly for their permission to use.
As for using Vimeo - by using Vimeo only, Community Education workers who dont use Vimeo wont have access to what you create. Collecting clips is the way to go. These dont need to be collected in an app as such. Collect on a device and edit once you have all the media you require. Once you have made your video, post on the required platform.
On mobile devices, Inshot is a good app. I use iMovie on a mac which i prefer.
I would add, i wouldnt post these across your own personal social media platforms. Anything me and my colleagues post are all posted across our services social media platforms.