Hi and welcome,
- OA is connecting, saying 'awaiting gamestate', then proceeds to load map resources, then goes back to defrag menu (most frequent behavior);
=> This likely happens because you have a conflicting Defrag version installed, or because the server is incorrectly set up.
- OA tries to connect and crashes with 'cannot load default.cfg' message. When I copied q3config.cfg to default.cfg, this happened
=> Probably same as above, default.cfg is a non-essential file and it shouldn't be required. It's weird it crashes for this.
- OA starts autodownload, downloads pak06-misc, map pak, then pak-06-misc-SOMENUMBERSHERE, then map pak, then misc again... ad infinitum.
=> This could be because the server itself hosts different versions of these files. If you check into your local directory, you may notice these files received different suffix which are checksums in order to differentiate one from the other. But it shouldn't go ad infinitum.
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Leave your connection as broadband, it shouldn't affect these issues...
You may try to install the OpenArena package from OpenArena.ws, Debian has its own way to manage files and maybe it puts a bit of trouble. It shouldn't, but that can help to determine if the problem is Debian specific.
Seeing OAX is because your OpenArena could run a development version of the QVM. But it happened Sago forgot to put the right version in that corner so this mention appears instead. The QVM (Quake Virtual Machine, the game logic which runs on top of the engine) is contained within the latest OA patch (which sometimes servers distribute by autodownload), and is also contained in main pk3 files of the game/
Your most noticeable problem is: querying dpmaster doesn't bring results with the ingame browser. You might give a try to xqf (it's in Debian repositories). There could be a problem with querying dpmaster because of your router if you have one.
You can try to move your ~/.openarena/defrag directory to something else, and try again to connect to some server. I fear not all servers run the same Defrag version.
Good luck with it.