Hi
From the Sineoutput example, how to change to the other waveform? Please help.

Do you mean triangle waves? You can do that by calling Tsunami.setOutputMode(OUTPUT_MODE_TRIANGLE);

What about an arbitrary waveform?

You can do this at low speed by calling setOffset with the DDS disabled, or (faster) by writing directly to the offset DAC using SPI. High speed arbitrary waveforms are not supported.

What would be the best way to generate a precise PWM signal? (i.e. the precision benefits from the precision of the onboard reference)

The TCXO drives both the DDS and the MCU, so you can set up a PWM waveform like you normally would on the Arduino and you'll automatically get the same degree of precision.