Question #1 Yes there is to be a screen there, and yes you can replace it…
Question #2 Fill her up sort of, if that makes sense, I have heard that if you get too much grease in there it somehow migrates up to block that water inlet…I have one of these but but as nice as yours.

Question #3 These older coils were really good, so might I suggest making good and sure the points are clean as a whistle, also check your condenser, I would suspect that once the points are spotless and rope it over good you "should" see spark.

I had the same issue with my latest a Johnson PL40, no spark, cleaned the points meticulously, clean around the circumference of the point faces as well, as I have seen points that the face was fine but had crud around the perimeter of the points that prevented it from sparking. Once cleaned properly she sparked.

Good luck and great motor

Richard