I recently purchased a Canon 100D and I'd really like to take a photo or timelapse the Milky Way. The current lens I have on my camera is the EF-S 18-55mm. Can this work?
For taking pictures of the Milky Way, you probably want to go reading through the milky-way tag here on photo.SE.
To do a timelapse, you want an intervalometer of some kind, which can automate taking repeated shots at a set interval. There are several types. Some cameras have them built in to the software (the 100D doesn't; although there may be a Magic Lantern development release of some kind that could add it), and you can also use smartphone apps (e.g., TriggerTrap) with a shutter cable connecting your smartphone to the camera; or you can buy a cable release that has an intervalometer in it.
Post-processing is going to be the harder part of the deal. Timelapse typically isn't done as a video (although, again, some cameras can do this), but as a number of still images that you then have to put together as a video. There's a variety of software to do this. But post-processing for shifts in position or color or exposure can be a bit trickier. I would say don't start out with the Milky Way as your subject for your first timelapse, but do something a bit smaller/shorter just to get a feel for it, first. Say, an ice cube melting, or sunshine travelling across the floor for an hour or two. Milky Way/sky rotation timelapses tend to be all-night affairs, and you want to make sure you get your technique both for shooting and post-processing in place before spending that much time on making one.
Yes it should not be a problem. You may want to have a look at something like a remote shutter control.
This way you can control the length/time the shutter should remain open while taking the photo
Also, it will be a lot easier to capture the milky way if there is not a lot of ambient light around (like city lights).
Have a look on Amazon or some retail site for a shutter release for canon.
Should do the trick.