Mixing Movies and TV-Shows
Technically speaking you cannot mix Movies and TV-Shows because of how they are named.
For example, a Movie doesn't have an episode number so the Scanner that detects your files and adds them to your Library wouldn't detect them in a TV-Show Library. The same with an Episode in a Movie Library.
What you can do is to add the files to your Specials Season.
However, doing that I would always try to compare what you are trying to do with how the metadata Provider does it. If you don't follow that example then you could end up with Plex assigning the wrong metadata.
Plex itself, doesn't really know or care about what the episode actually is. All it cares about is you following the naming convention. In terms of Metadata, it will assign the metadata to the episode regardless if that is correct. So, for example, when you have added the episode for "Some really cool episode" on S01E01 but the metadata provider has this episode listed as S01E02 then Plex will NOT add that metadata to your episode 1 (or fix it for you) but rather just add the S01E01 metadata to your S01E01 item so your S01E01 is now named "Pilot".
In regards to "Stargate SG-1" There are Some Movies in the Specials Season like "The Ark of Truth" (S00E05) or "Continuum" (S00E06) but not the original Stargate Movie. Source
This is from TheMovieDB which is used by default (unless you have changed it) in Plex Libraries.
You can set that particular Library and library item to use a different episode ordering, like TheTVDB. For Stargate, this might also be better because there you have the S00E01 as "Stargate" the first Movie, S00E07 "The Ark of Truth and S00E08 Continuum.
In terms of Playback, this could potentially also work with a "Next episode" so when you watch the original Movie in the Specials Season you would automatically get the "Next episode" from the TV-Show.
While this is possible here, it might not be possible for everything so keep that in mind putting episodes into the Specials Season because if some more Specials are being added, you might get Metadata assigned you wouldn't want (unless you lock it) or won't get those new specials listed in the library (or as duplicates).
How can I have one library called “Documentaries”?
You can use the same approach here with the same conditions and drawbacks.
Can I keep them separate to the movies/TV?
Collections are library-specific and are not "one for your whole server". So each library has its own set of collections that only display the items you added to that collection in that library.
However, Collections can reference each other across libraries when they are named the same. This means that when you have a Collection named "Star Wars Collection" in your TV-Shows and Movies Libraries, then you can see the Added Items from either collection. here is an example of what that would look like.
But keep in mind what I said above of them being "library-specific" if you change a Collection in one Library, this will not be applied to all of the other Collections.
Can I make a watch order collection? Have them in the broadcast order in one list? Including the movies?
No, Collections only contain the actual library items, so a Movie (in the Movie Library) or the TV-Show (in the TV-Show Library). When you want to have a "Watch order" then you need to do a Playlist and sort them there. Playlists CAN mix between libraries so you can add Episodes and Movies as you like.
Personally, I strictly separate Movies and TV-Shows and don't add the Movies as Specials since, IMO, they are Movies and not episodes. I then use Collections to group them together again in that Collection. I have also used Playlists to, for example, created a watch order for Battlestar Galactica but I haven't done that since.