Good points; all.
1). It is rather fussy, isn't it? I've tried all of the common shortcuts to gain finer controls. They're all dedicated to other functions, and Mac compatibility surely contributes to that. The closest I've come is in toggling between a Snap to 10 or 12 Levels to get myself in the general area, then fine-tune from there.
With the Step mode (in the Pitch StepGen), it's possible to hold a (external input) MIDI note, and make tuning adjustments 'by ear' with the mouse. Like the other workarounds here, the difficulty level increases with the number of Steps to adjust.
2). That's a great feature request. I'm unsure what the overhead would be, but the currently selected Step already does have the 'focus', so a division into the Depth value is required. I'm afraid that 0-100% would be confusing on those parameters that use cents or dB. I would think that some thought would have to be given to a conversion into currently used real-world values.
3). I may have some ideas that will help on point 3. Again, these are workarounds for a once-only phasing shift, but they could be of some use to you. The difficulties will go up with the complexities of the expected results.
a). With the MIDI Note Entry tactic mentioned above, it'd be easy enough to shift the source clip that you use for conversion into a Pitch StepGen sequence. For example, if you're targeting beat 2 in the project, you can chop off a few MIDI Notes from the tail, shift-select the note pattern forward, and tack those notes on at the head of the clip.
This assumes a final Sync setting in the StepGen. It's harder to explain than it is to see.
Here's some additional information. b). If you switch from a Sync setting to Freq, the StepGen sequence is triggered starting from the Note On itself. It's almost an envelope-type of behavior. You'll need to do some calculations between BPM and Hertz to make this work, though. For example, consider a StepGen at a Sync setting of 4 (beats).
If your host is set to 120 BPM, that's effectively 2 beats per second (120 beats/60 seconds). For Frequency, you'll need a figure based on one second of time, so that would be .50. 'Sync' is now based on when the Note On starts. Of course, there's all manner of calculators on the 'net for conversions of more involved situations.