I have a fireclay sink by American Standard (retrospect collection) in my bathroom. I installed it almost 6 years ago and I do have a small chip in it that has happened at some point. Since it sits beneath my medicine cabinet, I'm sure something was dropped onto it, causing the chip- I'm always dropping makeup bottles onto it! The great thing about it is that you can't see it and the only reason I know it's there is because I clean the sink and felt it with my finger tip one day. The sink is white, with the color the same throughout, obviously. When I was deciding between the two, I was told that fireclay was more durable. Considering the use of mine and the time it's been in, I'm pretty happy with it. I'm sorry I don't have any experience with Vitreous China to offer you.

I have never actually seen a glass vessel explode. It would need some very high temperatures to do that. Tempered glass sinks are pretty reliable, but if you dont use a mounting ring between the sink and the countertop and put too much pressure on it, it can definitely give the appearance of exploding as the tempered glass shatters. Here is a link that might be useful: Eden Bath Glass Sinks

The general range for the height of a sink is about 32" to 36" give or take. Vessel bowls vary from 4" to some I've seen that were over 12" tall, so you'd have to choose your bowl then size your vanity to get to your desired final height. An open or closed vanity may depend on the look that you're after. Clean slick contemporary? Something else? The choice really is yours, and the practical nature of available storage does come in to play. As far as chopping down an existing vanity, it depends on how much need to be chopped as well as the style and construction of the vanity. While it's easiest to chop the feet off or eliminate the tow kick on a cabinet, having it simply sit on the floor may look a bit awkward. While more difficult, it often look better to take material off the top, then add a new cabinet top that will compliment the sink. Then doors need to be changed as well. Paint grade you can dicker with, as the primer and paint can hide some scars. Stain grade, it might be easier to just get a new cabinet. Mongo

It's a rental. With that in mind, my go to choice would be an undermount. Second would be a drop-in. Never ever would I put a vessel in a rental. Do consider that if the vanity was designed for a vessel that any intrusion below the countertop might interfere with vanity storage. Draw functionality, etc. One sink versus two? If the bathroom is small, that might lead you to one sink. One person washing at a time, more counter space, etc. Plus, with your budget being tight? One sink will save you. If you think you'll have trouble renting this place and you think you might need an edge, or if you're renting to a couple/family, then two sinks could give you an edge in a tight rental market. Sometimes it's all about the bling. Just make sure that before you go the two sink route that the vanity itself can take two undermount sinks, or two drop-in sinks, PLUS the plumbing, without completely losing the functionality of the top bank of drawers in the vanity. If an undermount will cause you to lose storage, then I'd minimize the amount of lost storage by going with one sink.