Can the Android backup api be used to backup large files such as photos and videos? If so, is there a limit on the amount of data that can be stored in the cloud?
The Backup API is, as far as I know, made to store textual data such as preferences and notes and not things like images.
Take a look at Google Cloud Blobstore. It is a part of Google App Engine which you can use through cloud endpoints. Read the following links in order to get a sense of what I'm talking about:
Although this comes with costs, it is a very reliable and more versatile way of backing up images and such than Backup API is (and is made for).
See also the following stackoverflow answer, which explains how Backup API works and why it's better not to use it to store data unless it is essential for an install on another android device: