1) Snatch off the gag from thy mouth = take off the gag from your mouth (gag, refers to "Something forced into or put over the mouth to prevent speaking or crying out.")
2) And be free to keep silence = silence is your proper right, so you need not to gag yourself from speaking, just feel free to speak or keep silence?
3) Can you explain what "Made her neck and head
The top piece of a Nile obelisk" means?
She drew in her chin,
Made her neck and head
The top piece of a Nile obelisk
and said: Snatch off the gag from thy mouth, child, And be free to keep silence.
Tell no man anything for no man listens,
Yet hold thy lips ready to speak.
An obelisk is a four-sided, tappered column, the top of which is capped with a pyramid ion.
If she said, "Snatch. . ." then she isn't actually gagged, now is she? It's figurative in meaning: She's been told not to speak or feels she shouldn't speak. 'be free to keep silent' is explained in the lines that follow:
Tell no man anything for no man listens, Yet hold thy lips ready to speak.
Let the other person do all the talking, but don't let them think you're a push over. Speak if need be (i.e., stand up for yourself).