The Tecumseh points are #30547, the condenser # 30548A, the coil #30560.
Your condenser original had a ring terminal which fit onto the stud from the points. ....Your condenser was installed incorrectly, it is upside down. ....The condenser wire is supposed to come out on the bottom, snaked behind the coil mounting boss, and to the threaded stud. ....This keeps the condenser lead from getting pinched or chafed by the flywheel.
The ground wire from the magneto coil is slid onto the condenser hold-down screw, then through the condenser and threaded into the mounting plate.
The primary wire from the coil gets attached to the threaded stud of the points. ......The "kill" wire goes onto the spade terminal on the stud.
The ignition timing is set by loosening the screws holding the magneto plate and rotating the mounting plate (thus the slots in the mounting plate). ......Unless someone messed with it in the past, there is no need to check or change it. .......If you wish to remove the mounting plate assy, , mark around the screw heads so the plate can be reinstalled in the same location. .....Usually, you can visually tell where the plate was previously.
Clean any rust from the ends of the magneto laminations, clean the magnets inside the flywheel, clean the points & set the points at .020".
Those Tecumseh coils were pretty reliable, but they could fail. ....You can inspect the coil for cracks, and test the continuity of the primary and secondary wirings. .....Other than that, a magneto tester is needed to test the coil. .....New coils should not be expensive, but I may have a used one if you need one.