A:AnswerYes, you can run Ubuntu Linux on a Raspberry Pi and yes you'll need a MicroSD card for the Pi. Download a Raspberry Pi Ubuntu image from ubunto.com, flash it to the MicroSD card from a PC, put the MicroSD card into the Pi and power it up. Easy.
A:AnswerThe Pi is approximately 3.5" x 2.5" x .5" This does not include a power supply or any other "hats." You'll probably also need room for other wire connections.