No. The most amount of immunities after Shedinja is three:
Chandelure (Flash Fire)
Jellicent (Water Absorb)
I checked the type chart.
No, but Golett, Golurk, Drifloon, and Drifblim each have three immunities. I checked our Dual Type Chart.
No. There are a few Pokemon with 3 immunities but none with 4 (Besides Shedinja), unless you count Water Absorb Jellicent holding an Air Balloon xP