IIRC, I was able to operate the plunger from the playfield view by simply pulling back on the side of the playfield. You can test this by simply pulling back on the side of the playfield in TotAN right at the beginning when it zooms to show you the three holes of the skill shot. I always plunge on this table before the camera pulls back, because the first skill shot always seems to be top most hole anyway...
Weird, I've battled the Genie several times and always assumed the balls were being launched automatically.
To launch the ball during the restart, I only have to touch the screen. No sliding at all. That being the case, every time I hit the right flipper during the genie battle the next ball is launched (if there is one in the shooter lane).