In regard to question #1:
Take a look at the Symbol font in the Windows Character Map utility.
It has the integration symbol as well as some other greek and math symbols.
It might do in a pinch.
There are other latex fonts
out there but not many truetype with free distribution.
I recommend you create the font text symbols in a memory DC amd bitblt them where you need them in the equation (also works for text labels of graphs).
I do not recommend trying to use a richedit control.
In regard to #2:
BillSoo's: "How to Create a Line Graph
is a thread post with some simple line chart plotting code.
You can use VB's Line method to draw curves for plotting equations.
Forum thread on drawing parabolas: Parabola Program Help
If you want to reshape the curve you will probably have to drag around points.
For an example see "Bezier7d.zip" attached to this post
If you are looking for a vb6 calculus calculator & graphing code sample, see this psc code
In regard to question #3:
For plotting (and rotating) points in a 3D space the wireframe code attached to this post
might be a good starting point.