In case you need help showing inline buttons, here's how to do it. Go to the Customize Start Menu tab in Settings, double click the parent item (e.g. Shut down in this case) and check the option "Insert sub-items as buttons". They will show like this:
When you hover over the icons, the labels will show as tooltips.
You could try changing the setting "Large icon size" on the Menu Look tab from 32 to 24. It doesn't reduce the spacing between programs (that can be done by editing the skin) but more programs fit in the menu. After changing the size, you will need to exit the menu and start it again.
You can't have different sizes in two columns but you can change the padding for the second column separately from the first column. The value Main_padding controls left column's padding and Main2_padding controls right column's padding (the 4 values are number of pixels to add on left/top/right/bottom of the menu respectively).