But, given y, how can we get x? In particular does someone know a solution to x^3+7 = 0 on the secp256k1 curve?
Well, it's just a finite field, so this should work:
x = modular_cube_root ((y^2 - 7) % p, p)
I used the code
listed here to solve your particular example. It returns None, so probably there isn't an x that solves the equation when y is 0.