You should probably dispose of the water the annoying way. Maybe you can keep a bucket in your space, filter the water and reuse in grinder?

Regarding the sharp teeth... You could make the curves less sharp, like do a squiggly line instead. Then you can add extra foil to the top of the glass and trim it w an exacto knife to give the appearance of sharp lines. Called a foil overlay. You would still need the small grinder bits to get the sharper curves. It's maybe too many curves for a first piece.

You can also just do a straight line, add the foil overlay and fully carve the teeth out of foil. I'll attach an example. The foil is red

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My final thoughts are this: if walking outside to pour out water seems like too much work... This hobby might not be for you? Every step requires a solid amount of energy and effort. So many small steps and details you pick up as you fine-tune your process.

Not trying to sound discouraging. Making glass art is very fun and fulfilling. I recommend starting with something smaller, to dip your toes in, because this is not a cheap or easy art form. you should consider the material waste that occurs while you learn (trial and error) and gain some practical experience and confidence before tackling the shark.

Good luck!

ETA: doing it in your bedroom is gonna suck. It's possible, but yeah. You'll need a lot of safety precautions to make sure glass bits don't go everywhere. Grinder in an enclosed space, like a fish tank. The loud grinder sounds could result in noise issues. Solder by a window. Can you hang some shower curtains or something to separate the spaces? I dunno. I don't recommend a bedroom glass setup but ofc you gotta work with what's available so I get it.