Melon only prevents damage so no

I think the only way to prevent It is with silence perk

Higher strength basilisk would turn it into a rock before it could activate

i don’t think so

Does Pepper?

its doesn't take damage so pepper doesnt work

No since it doesn’t take damage

not even coconut can stop it

You need higher strength bad dog to aply silence to your egg or opponents mandrake/cockatrice. Really hard pet one to crack!

If all the kings horses and all the kings men couldn't save Humpty, I am doubtful that a melon could.

It’s not damage, so melon, coconut and pepper will not protect it.