When (and how) do I add a pre-packaged japanese curry to a slow-cooker

I've generally had success cooking dried beans in a slow cooker for about 5 hours on high with plenty of water (about 4 c. per 1 lb of beans). While you COULD add everything at once, I wouldn't recommend it, as the rest of your vegetables will become mushy and grainy.

For that exact recipe, I'd cook the beans in the slow cooker, than combine everything on the stovetop for about 45 minutes to get the flavors to combine.

Making a roux has two purposes:

1. Coat the flour granules with fat so they are able to dissolve into the cooking liquid without binding up.
2. Cook the flour to remove the raw cereal flavor.

When the cooked, fat-covered, flour is introduced to boiling liquid the starch granules swell and explode tangling up the cooking liquid. The cooking liquid is thus thickened and delicious.

If your roux is separating then the starch has not gelatinized. Because you saw this problem in the slow cooker and not in a pot I suspect that you are simply not bringing your liquid to a full enough boil to gelatinize your starch.

I have never seen a roux separate out. The roux should dissolve into the cooking liquid. You might check your ratio and make sure that you don't have too much oil in your roux. Variability in measuring your flour might account for why you see this intermittently.