Now, is it possible (and safe) if, say, I connected the output from the pins from 2-12 (according to this doc, it says each out supplies 40ma of current) to the motor, and then turn them all on to start the motor? Afterall, 10 x 40 is 400ma, pretty close to 500ma that the 5V pin supplies.
No that is not a practical solution to parallel connect 10 output pins together. Because you can’t insure that you can turn on all 10 outputs at the same instant in time there will be unequal current draws and short term short circuits. Besides in addition to the 40ma per pin limit there is a total package current output limit of around (I think) 200ma so you are not there that way even without switch timing problems.
You are going to have to learn how to utilize external transistors to switch currents. It is possible to find very low current draw 5v relays that the Arduino can drive directly, then the relay contacts can switch the higher current load on and off. But transistors are cheaper, faster and smaller then relays.