Can you insert an ActiveX control into your control project, and if so, what method is used to perform this layer of communication between the two controls?
Yes, you can. The method involved is COM Interop.
You used a PaintHandler delegate to paint your control. What is another method you could have used to draw your control?
You can override the OnPaint method provided by the base class.
How would you allow a user to both select a property value from a list and also have the ability to manually type in a value within the Property Browser?
Return False from the GetStandardValuesExclusive function.