in the solo form,when a hand moves towards the Southeast its Tsai and when it move towards the southwest its Lü, Northwest its P'eng.
Or something along these lines, is this accurate?

that only depends on which direction you are facing.

No.

"Cai" is plucking energy, a sharp inward jerking force.

"Lu" is rollback energy, taking force around your sides toward the rear.

"Peng" is energy that rises upward and away from your body.

Any technique in Taijiquan can be done with either (or both) hands to either side of the body.

Using force has nothing to do with compass points.