Axiom: More is Better; But when is more better?
You seem to be talking about (strong) monotonicity rather than non-satiation (which is closely related to but different from monotonicity).
(Strong) monotonicity says that we prefer one bundle to another if the first bundle has strictly more of at least one good and no less of any good. A bit more precisely and in a two-good setting,

Let $B_1=(x_1,y_1)$ and $B_2=(x_2,y_2)$ be two bundles. Suppose the preference $\succsim$ satisfies (strong) monotonicity. Then $(x_1,y_1)\succ(x_2,y_2)$ if either of the following is true:

$x_1&gt;x_2$ and $y_1\geq y_2$
$x_1\geq x_2$ and $y_1&gt;y_2$


So, to your Q2: If $x_1&gt;x_2$ but $y_1 &lt; y_2$, then (strong) monotonicity says nothing about which bundle is preferred. (This is not to say that the preference does not have any ordering over the two bundles, but merely that strong monotonicity alone won't tell us anything about this ordering.)