Our software can resize images to a certain height/width, which would decrease their file size a tad but there is no way to automatically say "all images must meet size x or resize them to that."
Our Team and higher plans include video encoding, which would very much provide an experience like Facebook, where the user can upload a video and we encode it to a common format so that all users can see it. For instance, if a user uploaded a WAV, we would convert that to MP4 so all browsers can view it.
Outside of that, the process is very much like Facebook for images. The only restrictor would be what you allow them to upload. Which if you connect to your own Amazon S3 bucket, the sky is the limit on size (So long as you are comfortable with the cost).