"Some of the stitches I have drawn with Horizontal ZigZag, Rotational ZigZag and/or Calligraphy appear to be broken up."
This can happen in 3D view with any of the zigzag stitches when the ZigZag Width is very low. You have drawn very short stitches close to each other, and this causes them to appear broken up in 3D view. Select 2D view and you will see the stitches. Hence, this is only an issue with displaying the stitches in 3D.
"I have chosen a variegated thread for drawing stitches, but only one color is showing."
Variegated threads are stored in the thread database as a sequence of colors, each of which lasts for a specified length. Hence, one of these must be the first color that is defined. While drawing stitches in 3D, only the first color defined for a variegated thread is used for drawing the stitches. When you right-click to finish drawing with the current drawing function, the variegated thread is drawn in all of its colors.
In 2D, only the first color of a variegated thread is shown. You must view your embroidery in 3D to see all the shades in a variegated thread.
"When I stitch out the embroidery, there is a thick group of stitches in one place."
This may happen if you pause the pen on the same point on the tablet for an extended time when drawing with Free Motion, Horizontal ZigZag, Rotational ZigZag or Calligraphy. Each of these drawing functions adds stitches to the design continuously when the pen is on the tablet (or when the mouse button is held down), as controlled by the Free Motion Stitch Speed. This is the same as holding fabric in one place in a sewing machine while continuously stitching. The stitches will be on the same point. You can see this happening as the stitch count on the status bar increases.
Either select and delete the excess stitches, or remove them with the Eraser.
Alternatively, mySewnet™ Stitch Editor includes a Density Advisor, which can automatically reduce the density where stitch points are tightly packed together.