Is there random assortment in metaphase II?
Metaphase I

Your understanding of the metaphase I is not entirely correct. In normal (human) metaphase I homologous chromosomes separate. Therefore, sister chromatides go together. More precisely sister chromatides are kept together at centromere. You have only two possibilities for each chromosome:

&lt;-AA   aa-&gt;


or

&lt;-aa   AA-&gt;


If we multiply the two possibilities for all 23 chromosome pairs it leads to correct number  223 of possibilities.

There can be one or more crossovers between two or more chromatides but the fate of crossovered chromosome arms is determined by the fate of centromere they get connected to.

Your diagram of random assortment, if I understand it correctly, allows for more than 2 possibilities for chromosome pair:

&lt;-Aa   Aa-&gt;
&lt;-aa   AA-&gt;
&lt;-AA   aa-&gt;
...


And it would lead to incorrect number of possibilities (more than 2)23

Metaphase II

In metaphase II sister chromatides separate as they would in mitose. Yes, there is random asortment of which chromatide goes left and which goes right. With your notation it could look like this:

&lt;- A   A'-&gt;
&lt;- b   b'-&gt;
&lt;- C'  C -&gt;
&lt;- D   D'-&gt;
...
&lt;- w'  w -&gt;


However, as I said earlier, some chromosomes can crossover more than once, so you can have thinks like:

&lt;- g''   g'-&gt;


or

&lt;- F'''   F -&gt;


or

&lt;- h'    h'-&gt;


Inverse meiosis

For every rule in biology there is an exception. Some species have inverse meiosis. This means they do it in reverse order. In metaphase I they separate chromatides and in metaphase II they separate homologous chromosomes.