This behavior can change. If you enable rotation, the first button is used for rotating fractals. Also, in fast Julia mode, the first button is used to change the seed.
If you don't have a middle button, press both buttons to enable emulation.
After few minutes of zooming you will probably exceed the precision and the fractals will get boring. If you are getting strange big rectangles on the screen, you probably reached the numeric limit: there is no way to avoid this except un-zoom back and choose a different area. It doesn't hurt so much, since you have zoomed approximately 64 051 194 700 380 384 times, so there are quite a lot of areas to explore. Algorithms with unlimited precision exist, but they are still too slow for real-time zooming.
The other possibility is that you have reached the iteration limit. The fractal is calculated approximately, and in this case you need to increase number of iterations used for approximation (and decrease the speed in the process). This is done from the menu or using the arrow keys Left and Right.
An Up and Down keys should be used to change zooming speed. Note that higher speed costs more and image will be blocky.
This behavior can also change. With palette cycling enabled, Left and Right keys change cycling speed; in continuous rotation they change rotation speed.
All other functions are available from the menu, which (in the default configuration) are displayed when you move the mouse to the top of the screen/window. It is useful to learn the shortcut keys, which are shown in gray next to the menu items they trigger.