Well, it seems the two of us share the wonderful challenge of having a Gym Leader and a Commander. 8D
Well I think Satomi and Edgar would get along well enough. Since both of them seem to have a facade of ice, I think it would be more a "What-are-you-thinking-damnit?!" contest when the two converse. xD Of course, I'm not sure whether Satomi will see Edgar as stronger than her... so they may just despise one another. xD
Ayumi and Purple on the other hand, I think will get along swimmingly. Though Purple will be weary bringing Buzz, Punch and Pie since they all have 4x weakness to ice, but maybe Toxic can frolic in the snow. Purple likes snow, so he'll be around every once and a while. :) Plus, I think Purple would invite Ayumi for coffee or something and they'd sit down and just chat, since Purple is one to chat if he's not currently doing his job. Furthermore, they both share an interest in co-ordinating! :)