Which of the following is correct?

Let $z = x + iy$ be a complex number,$A = \{z : |z| \leq 2\}$ and $B = \{z : (1-i)z + (1+i)\bar{z} \geq 4\}$. Then which one of the following options belongs to $A \cap B$?

$A$ point $z$ moves on the Argand diagram in such a way that $|z - 3i| = 2$. Then its locus will be:

Let $z_1$ and $z_2$ be two complex numbers satisfying $|z_1| = 9$ and $|z_2 - (3 + 4i)| = 4$. Then the minimum value of $|z_1 - z_2|$ is

Let $R$ denote the set of all real numbers. Let $z_1 = 1 + 2i$ and $z_2 = 3i$ be two complex numbers,where $i = \sqrt{-1}$. Let $S = \{(x, y) \in R \times R : |x + iy - z_1| = 2|x + iy - z_2|\}$. Then which of the following statements is (are) True?
$(A) S$ is a circle with centre $\left(-\frac{1}{3}, \frac{10}{3}\right)$
$(B) S$ is a circle with centre $\left(\frac{1}{3}, \frac{8}{3}\right)$
$(C) S$ is a circle with radius $\frac{\sqrt{2}}{3}$
$(D) S$ is a circle with radius $\frac{2\sqrt{2}}{3}$

The locus of $z$ satisfying the inequality $\log_{1/3}|z + 1| > \log_{1/3}|z - 1|$ is