Solution

а)
Let's surround the wire with rings of radius $2\pi x$, above the plane they carry current I and induction $$B = \frac{\mu_0 I}{2\pi x}$$, below the plane there is no current, therefore the induction is zero.

б) Similarly, over the plane the induction $$B = \frac{\mu_0 I}{2\pi x}$$ under: $$B = \frac{\mu_0 (I-I')}{2\pi x}$$

в) Using the same type of circuit, we'll analyze it. Inside the circuit, the current only enters. The answer is $$B = \frac{\mu_0 I}{2\pi x}$$
Let's take a wider circuit. The current enters it and the same amount exits $\Longrightarrow$ outside $$B = 0$$