New Post: Displaying shapefile points/coordinates at the correct location

Yes this solution seems to make more sense.

Using pixel makes sense if you're drawing something like MapFunctionMeasure or are trying to get something inside a certain radius whose size differs based on the zoom factor of the map.

Following your code above circleVertex seemed to be the coordinate you used to draw your circle around. Make sure that circleVertex and the layer you add your points to both have WGS1984 as projection. Furthermore don't call the following line of code but use circleVertex directly.

Point vertex = map1.ProjToPixel(circleVertex);

If you want your circle to be a MultiPoint feature don't add each point to features but create one Multipoint feature from all the circleCoordinates like you did in the code above.

As I'm normally working with meter based coordinate systems I have no idea how WGS1984 might affect your computations.