Answer: a), b) that is not possible.

a) Let us look at the numbers modulo $3$. Obviously, the amount of numbers divisible by $3$ cannot decrease. Because if both $a$, $b$ are divisible by $3$, then both $a+b$, $ab$ are also divisible by $3$. If one of the numbers is divisible by $3$, then $ab$ is also divisible by $3$. Thus, at the beginning we had only one number divisible by $3$, and in the end only one, thus such situation is impossible.

b) Let us look at the situation now when exactly three numbers are divisible by $3$. Thus those numbers equal $0$, $0$, $0$, $k$, where $k \in \{1, 2\}$ modulo $3$. Thus these four numbers will never change. Let us check now when the amount of numbers divisible by $3$ can increase. Then $a$, $b$ should be $1$, $2$ modulo $3$. However, then numbers $0$, $2$ appear. Thus in the situation where exactly three numbers are divisible by $3$, they should equal $0$, $0$, $0$, $2$, and four numbers from condition equal $0$, $0$, $0$, $1$. Thus we get a contradiction.