Given 2 points (x0,y0; x1,y1) and one angle (a): what formula will
determine the new location of point (x1,y1) if it were rotated about
point (x0,y0) through an angle of (a)? I need 2 formulas: "deltaX =
[something]; deltaY = [something]" where x1_original + deltaX = x1_new
and y1_original + deltaY = y1_new.

This one is pretty straight forward.  I'll use matrices to derive the equations:

Process:
  Shift points so that [X0,Y0] is at [0,0]
  Rotate point [X1,Y1] about [0,0]
  Shift back to original location

To shift the points to [0,0]

[X1',Y1']=[X1,Y1]-[X0,Y0]

A general rotation matrix is:

[x2,y2]=[x1,y1]*[cosa  sina]
                [-sina cosa]

Putting the shifted points into the rotation matrix we have:

X2'=X1'cosa + Y1'sina
Y2'=-Y1'sina + Y1'cosa

Translating everything back to the original axes we end up with:

X2=(X1-X0)cosa + (Y2-Y1)sina + X1
Y2=-(X1-X0)sina + (Y1-Y0)cosa + Y1

[X2,Y2] is the final location of the point
Note this is a clockwize rotation; to rotate counterclockwize use a negative angle.