Here's an approach...
First, however, is that to display both a box plot and individual points, you simply need to select both the box plot and the points symbol in the palette at the top of the graph builder. Same result as "right-clicking" and choosing "add points".
Re: showing dots only on selected box plots.
1. Highlight the points you don't want to display.
2. Right-click and choose Rows > Row Markers > Other
3. In the field that appears for you to type in the marker you wish to use, insert a space via the "space-bar" on your keyboard.
Re: different colors for outliers
You can create an indicator variable via a formula identifying if a data value is an outlier or not. Then you can choose unique colors/symbols for each of the groups ("Outlier" or "Not")
Example if you were doing the standard Outlier if it exceeds 1.5*IQR beyond the Q1 or Q3.
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