What is "Develes Te'enim"?
Rashi: When figs are moist, they are called Te'enim. When they are pressed into a ring, they are called Develes 1 .
Presumably, it says Develes Te'enim because one can make Develah also from dates (Ramban Hilchos Terumos 11:2). (PF)
Why did he use pressed figs?
Rashi (from Mechilta Beshalach va'Yisa 1): This was a double miracle. Even healthy flesh, when you put Develes 1 on it, it decays. Hashem puts something that wounds into what was wounded, and it heals!
Radak citing Tanchuma Beshalach 18: Similarly, Hashem used bitter wood to sweeten bitter water (Shemos 15:25).
What is the meaning of "v'Yechi"?
Radak (Yeshayah 38:21): It will heal. This is like "Ad Chayosam" (Yehoshua 5:8).