First of all, you can assume the server can infer this in a number of ways - there is actually no way to fully block it, but we can try.
The main issue for privacy is that it makes your browser behave in ways that are a bit too specific (i.e. less private by comparison with the rest of the browsers in the known universe).
As for techniques the site can use
- javascript can test the geometry of something that was rendered to draw conclusions - was this font actually used? test several options and check for variations
- measure font work between network events i.e. generate a site that makes the browser use unique links for 1) fetches a font 2) renders text and 3) only then another fetch - measure the time between 1) and 3) and draw conclusions. Repeat for test cases and draw conclusions - e.g. is the browser really fast using monospace vs custom huge font? not a great method, but not completely worthless
- some techniques can actually do some of this without Javascript, provided you can generate some weird CSS/HTML that conditionally triggers a fetch
By the away not downloading the fonts also makes you "less private". Some of this is a stretch but not impossible.
Now for a more practical problem. Lots of sites use custom fonts for icons. Which means some sites will be very hard to use, because they only display buttons with an icon (actually a letter with a custom font).
FWIW these two lines are in my Firefox profile to disable downloads and skip document provided fonts:
user_pref("gfx.downloadable_fonts.enabled", false);
user_pref("browser.display.use_document_fonts", 0);
If someone has better/different settings please share.
Finally the Tor browser folks did good work on privacy protections over FF. Maybe their issue tracker is a good source of inspiration https://gitlab.torproject.org/tpo/applications/tor-browser/-/issues/18097
Depends a bit on what you mean by p2p.
If you mean it as anyone can run their own server - this is already possible. But since message inboxes are one way you can really only control how the server for the messages your are receiving. The messages you send go to wherever the destination says they should go.
If by P2P you mean fully decentralized with no distinction between clients and servers then the discussion is a bit longer, but right now no, and for practical reasons probably not. Let me elaborate a bit.
First the protocol assumes a client, that is your messaging app, delivers the message to a server which is identified by a hostname/ip (you ability to deliver depends on this server being up and working).
For practical reasons the server is a separate entity, just like in email delivery protocols, because
Now, in practice nothing prevents your client and server from being the same machine, but if the previous two points are not true you will have a bad experience receiving your messages. Specially since most clients are on mobile phones, these two points will likely not be true.
Another thing we could do to get it to be fully distributed would be to run simplex on top of other p2p protocol - anything w/ a DHT that can expose ports to the Internet (Tor, GNUNet, etc). But this has one downside - the client app would need to recognize new types of inbox addresses and connect accordingly.
You could probably achieve this with Tor and some .onion host setup. But then anyone that wanted to deliver to you would need an equivalent setup.
Apologies, I tend to nerd on about distributed systems.