The technologies I've used in previous projects fully cover your requirements, so project success would be guaranteed and the progress would be predictable.
My experience in Image/Video Processing means that if you so desire now or in the future, I could add custom filters or other modifications to the videos.
I have developed, among others, a social network app that included comments, replies and likes,
it had an Android app as a client and an Elastic Search backend as a server, using REST API for communication, which is the what I intend on using in this project.
I've developed an Android app that captures the camera feed and filters it in real-time, so simply handling a video would be easy, I also have plenty more education and experience in Image/Video Processing.
The mobile app would be either pure Android or an hybrid solution depending on your Android/iOS needs.
The app would upload the video to a Linux server as separate files indexed by a generated filename.
The likes and comments, along with the video index, would be stored directly on a database, preferably MongoDB, but it could be some other either SQL or NoSQL database if you so prefer.