I couldn't figure out how to make a phalanx move. And what is the right click mode that turns on some odd graphics?

For phalanx moves, you just click the furthest piece from the destination space that's part of the phalanx (the line of pieces you want to move), and then click the destination space. Also, the "right click mode" is just for planning out future moves, so there's no effect to the gameplay. You can click on a space to create a circle on that space, and you can drag from one space to another to create an arrow.

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@ddyer you may want to check out the Abalone tutorial which goes through the interface and rules: playstrategy.org/study/AbaloneS