In the key of
C , going from
B resolves strongly to note
How should the note
D resolve? (To note
E? I guess it should be to note
C, assuming the key note has higher "priority". But what is the theory?)
Either one, really. It depends on the voice leading to a great extent. (I'm assuming common practice voice leading here.) Let's have a look:
The first example holds the common note (G) in the descant, and uses the usual G-C drop in the bass. The neatest place for D to go in such a case is to E; otherwise you're faced with a bare fifths sonority (which can be useful at times, but is ambiguous as to mode).
The second example substitutes V7 for the dominant triad, but maintains similar spacing. In this case, F follows its usual resolution to E, B moves to C, G in the bass drops to C, and D would normally go to C - you get a bare root and third sonority (which is surprisingly common in actual use). Doubling the third (E) is usually avoided, but not uncommon when required to work with motifs.
You could possibly take D to G, but it would have to rise to avoid parallel fifths, so D would need to have enough space to do so without crossing another voice - in this particular example, it would need to be in the descant.
The last example uses the first inversion of the dominant seventh. The usual voice leading applies: B goes to C, F to E, and the common tone G is held, so D goes to C.
There are other variations, to be sure: in common practice harmony, just avoid doubling the leading tone, avoid parallel octaves or fifths, and avoid direct octaves or fifths between the outer voices.
You can resolve D in either C or E (or G -- why not?). It doesn't make any difference.
Or, it does make a difference, it's just that you have to look at the context to see what fits better. But, there isn't any rule like there is for the leading tone. I mean B most likely will go to C, but D and G can go wherever. This depends on where the note is coming from and where you want it to go; you'll have to look at the melody as whole and decide.
I think you are under some misapprehension of what the word resolve means in a musical context.
There is typically only two types of notes that for the first while of your musical education you need to know resolves.
The leading tone resolves to the Tonic. ALWAYS!. There is some things to consider.
If a whole bar is say the dominant chord it is OK for the leading tone to jump around the voicings a bit and then when you move to a vi or I you can just make sure it resolves.
They are usually build on the Super Tonic and Dominant steps of the scale. Although you can when you start doing advance theory use seventh in all the various scale degrees. The leading tone chord with a seventh is also a especially pretty sounding chord.
They resolve to the note one space down.
So for instance in the key C Major the Super Tonic chord with its seventh will have the notes D-F-A-C No the C is the seventh note it needs to be lowered to resolve.
So it goes to the B (Leading Tone) Which in turn needs to resolve back up to the tonic. That gives you the chord progression of ii-V-I (Sometimes ii-V-vi)
The Dominant with its seventh is a bit more tricky. The dominant chord has the leading tone and in this case a seventh as well. Both these notes need to resolve correctly.
SO in our C Major Example we would have the notes G-B-D-F. B is the leading tone which needs to resolve to a C and F (Seventh) needs to resolve to a E. There is only two chords in the scale who would have those two notes vi (A-C-E) and I (C-E-G)
These notes that you mention don't 'resolve' in the strict sense of the word. They can move freely as you see fit but still within the confines of good harmony.
Hope that helps.