Here are a couple of examples of untrimmed bottoms on one of my vases. I do bump up the center slightly and roll the edge to create a bevel. This has the added advantage of providing a slight ridge to stop runny glazes.

Handle on cups

Recently there was an inquiry on a listserve concerning the advent of handles on cups. I found these Roman or Greek examples at the Carlos Museum at Emory University. Sorry for the quality. Hand holding a long shutter speed with no flash is not my best talent.