Oscilloscope test waveform, is to use the ground clamp to the ground of the device, the probe touches the signal to be measured, what type of waveform of that signal, not the oscilloscope can control. The oscilloscope is only responsible for faithfully displaying what it looks like.
Signal generators can output waveforms, and all of these waveforms you mentioned can be output. Jinhan Electronics' JDS3012A has the function of oscilloscope + signal generator, you can pay attention to it.