When I watch a facebook video, it automatically saves on iphone?

The direct apps control it to a degree. The iOS sets cache limits. The app uses that space to store many things. It uses the cached items to enhance your user experience.

For example if Facebook took a minute to load, would you use it? Probably not. So, files are cached so app can open quicker, videos load and play with no glitches etc. It all leads to better user experience.

Apple OS and apps use their own space separate from third party apps.

No, the Facebook app caches segments of some or all video displayed in the app. This increases performance by using less battery capacity, reducing stuttering etc. The app maintains its cache and periodically deletes older its. Please look at my FB app below,

FB is caching and temporarily storing over 200 MB of videos, photos and other data to provide a better user experience.

You can force delete the cache by deleting the app, downloading a fresh copy and logging back into your account.

Chronological order requires you to log into your Apple Community account.

No, Facebook decides which videos, photos to cache. It favors your content and most recently viewed content. Some content may not be cached.

Each app will cache files slightly differently. Cleaning the cache is coded into the respective app by the app developers. Yes cache is cleaned, but you can force the deletion of the cache by deleting the app.

no, it streams as in send you frame by frame from the server which are displayed and then replaced by the next frames as they are sent

No, not on an iPhone or iPad. Many times they are stored in a proprietary format and private areas of the app.