Quick way to check and see if the points are opening... use a test light. Check to be sure you have power into the coil (steady light) and then probe the coil wire terminal to the points side while cranking. If the light flashes then the points are opening and closing and receiving current (voltage). This isn't an absolute check. You could still have issues with the condensor, weak coil.. etc. Your just looking to see if you have potential for spark.

You can also invest in a spark plug checker.. &quot;TEKTON 5889 12-Volt In-Line Spark Tester&quot; would be an example. $4 cheap tool that can be invaluable.

Once the cap and rotor are off, the dust plate will pop up. The distributor is notched to allow the plate to fit in one way without allowing it to rotate, get yourself a small screwdriver or something similiar and at the notch pop it out. 

Your button is getting hot due to the amperage draw through it and the resistance. For good cranking with any 6 volt system, clean terminations and proper sized cables (wire) is a must. The bigger the cable the better. Just be sure your not using battery cables sized for a 12volt. You really want 1 or 0 gauge. 

You can drain some fuel off the bottom of the carb to check that your filling the float bowl, but that won't guarantee atomization. Pull a plug and see if its wet. My guess since you've indicated it won't fire off a sniff of ether that your on the right track and its ignition related. 

Good luck... you'll get 'er.