a. From the structure, it can be seen that it contains two methylene groups and is a tetrahedron structure, so it is impossible for all atoms to have * * * planes, so A is wrong;

B. The carbon atoms with four different groups are chiral carbon atoms, and obviously there are no chiral carbon atoms, so B is correct;

C. According to the structure, there are seven kinds of H in the molecule, so there are seven different peaks in the NMR spectrum of A, so C is wrong;

D. Phenol -OH is acidic. When it reacts with NaOH, the ortho position of phenol -OH reacts with bromine, and -NH- reacts with bromine water to form salt, so 1mol of methyl can react with 1 mol of NaOH and 3 mol of Br2 at most, so D is wrong.

so choose B.