How many pet slots can we get through the use of mystical montre/donadak plushies? And to this max. amount, any slots that might be obtained from loyalty boxes are added, right?

This sticky in the Subeta Pets section should help. http://www.subeta.net/forums/view/575712

Depending on the plushie I believe it's 1 or 2 extra slots.

Thanks!

I believe I've seen people with more than 20 slots, did they get those by using plushies to get 20 and then using loyalty boxes? Or is there another way to get so many?

right now the only way to get over 20 slots is by using loyalty boxes for slot and thereafter.