Are those properties sufficient for defining a field?

These axioms do not require the existence of the opposite (for addition). The set of the not negative rational numbers with the usual operations satisfies these axioms and is not a field.

No. You still need additive inverses and the two associative properties. As a quick counterexample, consider the set of all nonnegative integers reals $S=\{x\in\mathbb{R}\mid x\ge0\}$. They satisfy all six properties. But it's not a field because there are no additive inverses.