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I have several 2D points in latitude and longitude coordinates (in decimal degrees).
I want to plot them into a JPanel canvas.
Since latitude and longitude are coordinates in a sphere or ellipsoid surface,
do I need to convert them to cartesian coordinates (linear surface) first?
For a correct presentation: yes. You need a projection to a 2D surface.
If the coordinates are all in a rather small geographical area and accuracy is not a strict requirement, it may be OK to just interpret them as pseudo 2D coordinates.
Have a look at OpenMap. I used it for drawing small maps, wasn’t too difficult. (and once you’ve plotted your coordinates, sooner or later you might be interested to add some political maps or other shapes)