Some doubts about netput vectors
We say that $x \le y$ when $x_i \le y_i$ for each $i=1,\ldots,n$.
If the production set can be represented by a production function $F$, and $F$ is homogeneous of degree $r &lt; 1$ ($F(\lambda x) = \lambda^r F(x)$ for $\lambda &gt;0$), then the production set satisfies the non-increasing returns to scale property you state. Moreover, if $F(0)=0$, and $F$ is concave, the production set also satisfies non-increasing returns to scale. Hence, you can think of the definition as a generalisation of the intuitive understanding you have.
An isoquant takes the output level as given and specifies all the input combinations that give you exactly the given level of output. The transformation frontier is the frontier of the production possibilities set. The production possibilities set takes the inputs as given and specifies all the output combinations that are possible for the given inputs. You can think of the transformation frontier as the output bundles that are not wasteful (i.e. efficient).