A major part of the sound to get these is the specific tonal relationship between the operators you're using. FM8, Sytrus, Operator, or any other FM synth will work, as will synths capable of FM like Serum. If the synth can do Amplitude Modulation or Ring Modulation (AM or RM), even better.

Try modulating square wave or a sine wave by a saw wave or another harmonically active waveform that's a perfect fifth or perfect fourth away - either five or seven semitones up or down, depending upon where you wanna go, increase the unison so you can get a wider sound, then slap a low pass filter on top with a quick decay and no sustain. If you're still not getting the sound you want, reverse which sound is the carrier and which sound is the operator.

Some of the sounds will be FM specifically, others will be AM or RM - they'll all get you close to the sound you want, so just experiment with waveforms and modulation modes until it sticks.

You don't - The waveforms are whatever pitch you play the notes at. I definitely suggest taking some time and going over the massive user manual if you haven't already.

You'd be using the modulation oscillator - set it to +5, -7, +7 or -5. That would be a fourth above or below and a fifth above or below, respectively. Phase is just frequency modulation, so use that or Ring Mod on your oscillator then pluck it with a filter.