I've noticed this most on certain Lugormod servers. Lugormod has an intelligent AI system for bots that makes them behave and respond to your actions almost as if they were real people. For example, turning off your lightsaber will make them stand by you, and meet you, and not attack you. They will also answer to certain simple questions as if they were real people. I've found myself fooled, and chatting to the air this way at first a few times... >.<'
The thing about JKA is that it's been around for so long, and the community has evolved so much, it's hard for us to relate to the very beginnings. But most of us are very helpful, so if you have any questions, don't be afraid to ask.
In terms of competitive dueling, you can still occasionally find dependable, base-game styled competitors who value a vanilla, fair play above all, but more often than not you'll encounter competitors who use enhanced 'tricks of the trade', some of which may have once been considered as 'laming' and 'hacking' the game. These tricks give them an advantage over standard competitors -- such as triple and quadruple hits by spinning with a heightened mouse sensitivity applied, but they are consistent as a competitive practice. If you find yourself facing a lot of these competitors, you can either choose to join in the fun, and try to learn these 'advanced/hacker' practices, or simply turn away and find a server with 'normal' duelists. Whatever you do, don't get upset over it. Everyone has a right to play the game the way they like.
As for disappearing servers, this can be due to one of three reasons:
1. You're not using the same version of the game. OpenJK has a different server list to retail 1.01, and retail 1.01 has a different list to 1.0. I've noticed that the Mac retail version also often shows a slightly different list to the Windows version. I recommend using OpenJK, as it's the most up-to-date for Multiplayer, and seems to be consistent and reliable across the different platforms (Mac/Windows/Linux).
2. JKA is old-school -- you have two buttons that operate the server list. One for refreshing the current server information, and one for populating the server list with new entries. Make sure that you get a new list each time you're looking for a server. Sometimes you need to do this twice if there's an interruption in your connection to get the full server list of currently available servers.
3. The server you have joined previously is not a reliable server. Running a JKA server these days is low-cost, and relatively easy to set up, so there are a lot of servers that are temporary, or periodic. That said, there are a lot of servers that are steady and reliable as well. You just need to get to know the steady ones over use/time.
Note that you can favourite a server, and that will register and save its IP address into your client, to the Favourites list. This works particularly well with OpenJK, as in the retail versions of the game I've noticed there is a bug that causes your favourites to disappear from time to time. In OpenJK I've never lost my favourites, and it shows me when the server is down, too, so I can follow its uptime. (When it is unreachable, it will show the server's IP address instead of its name.)
You can also search for a user's player name, and follow them to the server they are logged into. This is not always most up-to-date and reliable, but can help when you're looking for each other in the vastness of the server list.
For transitioning from SP to MP, I remember one of the first things I had to learn was to use the katas/specials sparingly -- very sparingly. Some people even recommend not to use them at all. They leave you very exposed to a well-timed, one-hit-kill attack from your opponent. I still use them occasionally, but only in well timed circumstances, where I know my opponent's reach for a well-timed counter-attack is not optimal, and where using the kata/special really has an advantage. I do not use them against a very experienced opponent who knows how to easily counter them, however! That will surely get you killed in no time. The trick is to keep your attacks unpredictable.
In general practice:
Red/Strong breaks Yellow/Medium form on direct hit, and easily breaks through Blue/Fast.
Yellow/Medium breaks the Blue/Fast form on direct hit.
All three forms have their advantages, and can/should be used in combination skillfully to surprise and outsmart/overpower your opponent.
In common sense, for your sake, you do not want to jump into the middle of a Red/Strong swing -- you want to stay away from it, and counter-attack from the side or back while your opponent is vulnerable.