Taranis

At least for me the name of the launcher file changed with this version. If you are using a shortcut to start the launcher, then you have to update the shortcut or create a new one.

No, the soundlag is clientside. So if your players are walking into a "wall of lag" when they walk away from running machines then turning off the ic2 sounds could help. For the solar panels you could try to use the Compact Solars, they are already part of Tekkit. With them you can pack up to 512 solar panels into a single block.

Have a look at this: ThisLogMustDie Should be doing what you are looking for, unfortunately the oldest version is for Craftbukkit 1.1-R6 so I have no idea if it is working Tekkit. Somebody who knows more about Bukkit than I do maybe able to answer that.

If you have a railway between both locations you could transfer the energy with an Energy Cart

Do you stop or restart the server without using the "stop" command by any chance?

I don't think so. From the Minecraft Wiki: At least my Tekkit server came with a view distance of 10 set in the server.properties by default. So a single player amounts for 441 loaded chunks. A second player, that is twice the view distance away from the first player would double the loaded chunks to 882. 126 chunks seem insignificant then. There are some other things, that could cause lag. Do you have large industrialcraft solar arrays on your server? You could also try to turn off the sound of your industrialcraft machines. (Open the IC2.cfg file located in %appdata%\Roaming\.techniclauncher\tekkit\config\ and change soundsEnabled=true to soundsEnabled=false) I've also experienced redpower2 timers set to a very low frequency causing lag as well as buildcraft redstone engines running in the red state pumping liquid with a wooden waterproof pipe.