I my experience with UK visas, although not in the USA, they arrange shipping for your passport, and send your supporting documents separately - using whatever you sent in. So yes, if you don't send a shipping label you don't get back your supporting documents, but will still get your passport.
You raise two questions.
The uk.gov page uses the term "documents" to refer to the whole packet, i.e., the application form, your passport, and supporting documents. I can understand only wanting the passport back, but were I you I would want to avoid a semantic dispute with VFS about whether the word "documents" includes your passport or not. For the ...
If you have a 4 hour layover, you may need to pass through immigration and leave the terminal but that’s easily doable in 4 hours.
Here are the Post Office details at Heathrow:
The airport Post Office is on the first floor of Terminal 3 departures, in the public area before security ( it's near the security control entrance).
Opening hours: Monday ...
You can use Poste Restante in Sweden.
PostNord (the nordics joint-venture postal organization) has an info page about this. Find the best Poste Restante post office and just send the message there with your name on it.
I've used it a few times and it's almost always working.
As far as I can see you should be mailing to a different address:
You should mail your application to:
VFS Services USA Inc.
UKVI Scanning Hub
145 West 45th St Floor 5
New York NY 10036
According to the UK Government website