If it's only used for printing models, and not anything that will be inserted orally, I don't see a problem. But I think the answer would be rather subjective.

Just because someone uploaded something to Thingiverse doesn't make it safe. If you were to attempt this, though, it'd probably be safest to use uncolored ABS because its glass point is higher than PLA and you never know what's in the colors.

Another problem is that it takes too long to switch from one color to another, since the old color has to be purged. A comment on the guy's YouTube video says it takes 100mm to fully switch colors. That would add up to quite a bit of waste.

One could print two halves and fuse them together. The seam might be nearly invisible after polishing. With an FDM printer, a hollow ball is less of a problem because the arcs of the sides and closed circular layers would tend to hold things together. A hollow box, however, would be difficult. You'd have a large, flat area with nothing to support the middle. I'd probably print such a box at a 45° angle if I had to, so that nothing is horizontal.

ABS filament tends to absorb water over time, so I would think and ABS part wouldn't hold up.

This raises the question of what the original part was made of, and whether or not that material be used in a 3D printer.

That is true. My answer comes from my experience modifying my FDM models to work with Shapeways, which uses laser sintering, as described in the question.

So, it appears the "perimeter" is actually a brim. I've never needed a brim so far, and based on your image, I would say that you don't need one, either. I think Tom is right about the rest.

I've never seen that kind of lifting, but are you sure that's perimeter on the outside and not a skirt? My best guess is that either the filament diameter or nozzle diameter is wrong in Slic3r.

There are clamps you can print on Thingiverse. You'd have to browse for the right ones for your printer and the thickness of your glass.

I don't think you're likely to lower the baud rate to the point where it's slower than the actual machine. Lower baud rates can be a good thing if there's a lot of noise in the signal, such as can happen with cheap cables. It's like talking more slowly to help someone understand you. I prefer to simply use the SD card on my printer and take my PC out of the equation.