No, there no pedestal.
Yes. http://www.homedepot.com/p/KOHLER-Archer-Self-Rimming-Bathroom-Sink-in-White-K-2356-4-0/100604966?MERCH=REC-_-product-1-_-202493976-_-100604966-_-N
Vitreous china
This model has a faucet that is 1-3/8′'D.
I believe you will only need to cut the base corners to accommodate. Buy the sink and bring it home, as we did. OUR PROJECT: dual sink replacement on small tiled counters. I studied the posted online dimension details of the new sink basin before our purchase. I got under our counter and measured it too... Seemed totally compatible with little change. Our prior sinks were overall 19” diameter from 1970. After sink removal and plumbing caps....We were able to cut the base corners of the tile counter to accommodate the 2 new rectangular sinks, which have a wide and supportive frame. We did this part on our own with cutting tools! We did NOT use the template provided with the sinks, as we found the cutout suggested was much larger than the minimum change we needed on site. We then called the plumber back to hook up the clean & new plumbing under the counter. Great update. I highly recommend these sinks.
22-3/4" wide by 19-1/2" deep
I know it's available in the store as of March 2020. Not sure about online.
Some single handle faucets (at least kitchen faucets) come with a cover plate that fits between the sink and the faucet. You can put the plate on then attach the faucet. Check the faucet you are buying.
Our sink cabinet is 21" wide and it fit fine.
None.