I'm no expert but I would think that if you can get an overflow drain that will accommodate the thickness of the material it would be easy to add the overflow/drain setup to the stone. I know in the local tile shop they have a travertine carved tub but I don't know if there is an overflow or not. A plumber could probably make something for the overflow and drain, or add length to the overflow/drain fixture, or have it made. I made my own SS sink recently, but without an overflow, and set my own drain. I followed along with the Buck's County Soapstone video to draw up my plans (with a lot of stop and starting of the YouTube video). They used a Kohler sink drain that could give them the depth that is needed for the stone. But even still I needed to take material out around the drain to get the hole thin enough to accept what I think was a 3/4" thickness for the drain and nut. So that is what I used. Taking out material also allowed me to create a slope to the bottom for drainage. So slope might be something to consider. I don't know how much slope you would need for drainage - probably around 2% at the min.? I haven't done the length to figure out how much material that would remove if you did it with a flat bottom. You don't want to get it too thin at the drain end. Unless, you put the drain in the middle near the back long side then you could split the difference. BTW, My sink holds water too :)

Tilex, I had a mildew problem in a bathroom and it cleaned up great. Just make sure it's venilated well in there, it has a strong smell to it.

After you find a faucet you like, see about getting that same faucet with a stopper drain and a lever in the faucet body to open/close it. A very common purchase combination. The new drain replaces the one you just got, which you chuck out or give away. yes you can turn the sink around. There are no police enforcing sink orientation one way or the other. A drain drains the same too. Turning it around helps you see less of the chrome overflow drain cover. (Replating it is always an option.) Sooner or later someone might post a link to a web site where you can order cheap overflow cover plates with various finishes. Never gone looking for it myself. Post what you yourself can find. hth

Probably some lint stuck in the short rise and horizontal run after the trap. It could also be from burs left on the ends of the cut pipes and not removed correctly. It takes almost nothing to catch the very fine lint in the wash water and start to build a clog.