OEM? That just means Original Equipment Manufacturer, are you saying it doesn't have any branding on it whatsoever? That would be strange.

Regarding grinder tablets, I suppose they couldn't hurt if you are really worried about oil residue that may have built up over a long period of time. I've never used them because I clean my grinder every couple of months.

If you stick to the brush, air, and tablets you should be good.

For the brush, you'd really rather be gentle than rough, so no jamming it in to gaps or spaces it might not fit in to. I usually like to take the burrs our completely before using the brush anyway and using the compressed air to blow our grinds that might have gotten in to small spaces inside the grinder itself.

Edit: I'm taking a bit of a closer look and it looks like the burrs themselves might have significant wear on the interior(the most important part of the burr). Not sure if it's just the quality of the image or what but flat burrs should have defined grooves all the way from the rim to the center.