Moving between staff voices - issues

"The cursor moves to the beginning of the bar when it should logically move to the nearest note of voice 2.".
I try to understand, but for now, your "logic" is not obvious for me. Why move to the nearest note of voice2? If you want to go in voice 2, select a note in this voice 2, that's all. Perhaps you are familiar with the operation of other software? As said elsewhere, a period of adaptation and understanding is needed.

And this is related to your point (b):
If you want to navigate into the voices, simply begin to select the note in the "good" voice '', and the cursor works fine as expected.
To illustrate this sentence: in you example, instead make x operations as " In Edit mode, select the first note in bar 11, voice 1. Go into note mode. Switch to voice 2 (by clicking on the voice 2 button). Now press [right arrow] to move the cursor. The cursor moves back to voice 1 rather than staying in voice two", you have just to begin by selecting the first note in voice 2, i.e, the bass D, and then the cursor navigates in this voice 2 as expected.
And if you want navigate into the notes of Voice 1, make the same: select a note belonging to this voice 1. "Logic", right? :)

It helps to realize there are two different things that act like cursors in MuseScore. The colored box that appears in note input mode shows you where the *next* note will be entered and is colored according to the vocie you have selected - which controls the voice of the *next note you will enter*. But there is also a highlighted note that is *selected*. This note may or may not be within the box, and it may or may not be in the same voice as whatever you have said you wish to enter next. When you use the cursor keys, it is the *selected* note that changes, so if it is in a different voice than what you have said you want to enter next, the new selected note will be in the voice of the old selected note. Since you presumably also want the note input cursor to move, it makes sesne to change its voice to match.

Selecting a note and then clicking a different voice in the toolbar actually switches the note into that voice. Try it with voice 3. The only reason that wasn't happening when you did (b) is that voice 2 was already full.