Hi Skamath,
Whilst I don't have any pictures to hand, I will do with those available online.
Small plastic spacers/plates are included with Beastgrip and screw into the brass mounts as this picture shows;
This fits in between the phone body and grip to ensure that the lens is flush with the hole in Beastgrip so it has a decent viewing angle of any lens etc that you attach.
There is a few mm's of space between your phone lens and whatever lens you attach to Beastgrip, however you do not need a DOF adapter unless you are attaching SLR lenses. If you intend to attach a Wide Angle Lens or Macro Lens etc you will either need to buy them in a 37mm fit or buy suitable step up rings to ensure they screw on.
Lenses such as these will not require any modification (obviously within reason, if you get a lens that is too big you may need to add a macro tube to ensure it does not get caught by the grip itself)
Baby Death 37mm 0.3x Extreme Wide Fisheye Lens + Filter Kit for Skateboarding | eBay
37 mm 37mm 0.45x Wide Angle Lens Converter + Macro for Canon Sony Panasonic Fuji | eBay
I hope the above helps
You mention Snapzoom and Beastgrip, they serve 2 different purposes. If you want to add a high powered zoom then use Snapzoom, however with the Lumia 1020 I would say Beastgrip is a better fit as it allows you to attach a wide range of photography accessories, such as lenses, mounts and lights (hot shoe mount).