Here to help.
1 The Falling Baker sketch featured 1 wedding cake at the end, so yes it exists.
2 Yes, there's a Number of the Day with the Count at his Counting Organ for the number 1. He plays the note, and the low grave voice sings out 1. And then the thunderclap or noisemaker effect starts up.
There's even a sketch for the number 0 where the entire organ gets blown away. In fact...
Under the current Season 36 scheme, this Counting Organ 0 sketch where the organ gets blown away is being used for 0, the revised Song of the Number songs for 1 through 10, and a new song with the Count singing to Countess Dahling van Dahling with her yelling out "SCHTOP!" for I believe 11 and higher.
3 The sad thing is that the Counting Organ doesn't have a sketch for the number 21, the highest number ever featured as SS's Number of the Day.
Oh, and there are a few other 1 sketches you might wanna check out.
Song sung by Johnny Cash about the legend of the Count as a Western character, starring The Count, Countess Dahling van Dahling, and Big Bird in Western outfits.
And the episode where the number 1 doesn't want to be the number 1 any more.
Hope this helps.