Does there exist a closed Moishezon manifold with zero second Betti number?
If $X$ has positive dimension, the answer is no. In fact, the following holds:
Proposition. Let $X$ be a compact manifold such that $a(X)= n >0$. Then $b_2(X)>0$.
The proof is essentially based on the well-known fact that the assumption $a(X)=n$ implies that $X$ is a bimeromorphic modification of a projective manifold. Look at Lemma 1.4 of the paper
Campana, Frédéric; Demailly, Jean-Pierre; Peternell, Thomas, The algebraic dimension of compact complex threefolds with vanishing second Betti number, Compos. Math. 112, No. 1, 77-91 (1998). ZBL0910.32032.