I had the first completed but when doing its converse, since there is no CQ rule, I do not know where to proceed. Please help
As usual the key is to work backwards.
To introduce the universal, assume an arbitrary variable, $a$, then derive $P(a)\to\lnot Q(a)$.
To introduce that conditional, assume $P(a)$ then derive $\lnot Q(a)$.
To introduce that negation, assume $Q(a)$, then derive a contradiction.
To derive that contradiction under the assumptions of $\lnot\exists x~(P(x)\land Q(x))$, $P(a)$, and $Q(a)$, well...