One can learn to play the piano on an electronic or midi keyboard with closed headphones without waking up the roommate. Is there anything equivalent for drumming? Some sort of nearly silent drum pad or percussion set with midi out?
Professional electronic drum kits are made by many musical instrument manufacturers including Roland, Yamaha, Alesis, ddrum, Simmons, and even the Zildjian cymbal company. The link in the previous sentence goes to a list of kits sold at Guitar Center.
These are all "silent" in that they make no sound acoustically (however you can hear the sound of your drum sticks striking the plastic drum trigger pads, which do not resonate). When you strike a drum trigger, the "brain" in the electronic kit plays digital samples of acoustic drums, or physically-modelled sounds that mimic the sound of acoustic drums. To hear these sounds, you need to plug in headphones or cables connecting to an amplifier and speakers.
While they can be used for silent practice, the main purpose of these drum kits is twofold: to enable a drummer access to a much larger range of drum sounds than can be found in an acoustic kit, and to enable concert performance without the need for using multiple microphones all over the kit to amplify the sound. Rather than needing microphones, you simply run cables from the "brain" directly into the PA system, while the drummer hears what he is playing through monitor speakers.
Yes, there are electronic drums.
There will be a tapping sound when playing. This will likely not disturb your neighbors, but your room mate might find it disturbing.
I believe that playing with brushes is problematic, but I'm not updated on the technical advancements of electronic drums.