A little late, but seeing as I've done this recently with a Mahr 817 (Didn't consider the Tesa because they've never responded to my inquiries in the past).
1. At least the Mit (and the Mahr) have a counterweight securing screw in the top. You have to remove the stylus, fully lower (and hold down as it will float up) the carriage, and then snug the counterweight retaining screw in the top. It doesn't need to be more than hand tight, but it needs to be done.
2. I have mine in a hard sided SKB golf club case, fully packed with a firm foam. This is also how the Mahr reps ship and fly with them.
3. When it showed up new it was in a substantially oversized triple walled cardboard box with cardboard angle reinforcing all the edges and strapped to a pallet. It was supported by a few foam ribs, which is much more compliant than the nearly solid foam packing I normally move it in. Honestly this is probably easier on the instrument, but does require a bit more space for it to float.
Here is a picture of the factory packaging (minus the box) on the left, and part of the case I move it in on the right. Click to enlarge. Note, the screen was not attached as-shipped.