I'm still abit confused. Can someone tell me what brushless, brushed and stepper motors are? What are their differences? What applications would be best for them? What are their disadvantages and advantages?
This doesn't give you enough information?
Seriously - there are ton more kinds of motors than you mention, and that wiki article does a fairly good job at giving a decent overview on most of them...
ok so to control the speed of a brushless motor i would use an esc. but then if i connect this to an arduino and i wanted to constantly alternate the direction of the motor every 2 seconds, how can i do that? also how do i find out the amount of torque in a brushless motor?
Depends on the sort of BLDC - if its a sensorless like all the RC ones then reversing direction isn't viable. Hall-sensor BLDC is needed for that if brushless is a requirement.
For specifications of a motor you look at the motor specifications. Simple. -
[ edit: Actually it helps to know about the relationship between Kv (voltage constant) and torque constant. This is trivial in SI but noone quotes Kv in SI alas (radians per second per volt). The torque constant (newton-metres-per-amp) times Kv = 1 (for an efficient motor). Thus a motor with Kv = 1800 rpm/volt (188 rad/s/V) has torque constant of 5.3mNm ]