With a grenade, it's not the explosion that kills people, it's the shrpanel. It's pretty much impossible to be killed directly by a shockwave. The shockwave might accelerate a piece of debris, which kills you, or you might be accelerated, then pushed into another object with enough force to kill you, or the air might be hot enough to burn you to death, but the pressure itself is not going to kill you.
Depends on the type. The old "pineapple" type worked basically through the scrapnell, but the type used in most European armies is a HE type with only limited scrapnell from a thin shell. The main effect comes from the shockwave generated by the 180 grams of TNT inside it. The idea is that it is less dangerous for the one throwing it, and it works very well in pill-boxes, and in columns of soldiers.
ETA: If you don't think shockwaves can kill, you have not seen uncensored videos of the clean-up work after terrorist bombs. I have, and I don't recommend it, but it is something about scattered body parts and de-fleshed skeletons

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Keep in mind that, for normal sounds, the pressure differences are rather insignificant when compared to the base pressure. For instance, the noise of a freight train raises the air pressure to 100.0001% of its normal value. So yeah, a loud noise probably does travel faster. But only by .0001%.
The effect of an explosion is quite different than that of a loud noise. Otherwise, obviously, explosions could not demolish anything with more effect than loud noises can. And as we know, they can. For instance, the reason a HE detonation can smash through concrete is that the air pressure is so high that the shock-wave has "foot-hold" to propagate into the concrete.
A "shock-wave" isn't actually a wave, according to the physics meaning of the term; it's a pulse. So "wavelength" isn't exactly an appropriate term.
It is a pulse edge. However, any pulse edge can be resolved to a frequency spectrum, so wavelength, or if you want to be very precise, wavelength
s,
is an appropriate term.
Although, if you were to record an explosion from a bit of a distance, you would see a ringing (containing a number of frequencies).
Hans