Is there an adaptor that can make a EF S lens work with an EF Camera?
No. And there are several good reasons for this. There are actually ways to make it work, but it's a bad idea.
The "S" in "EF-S" indicates the lens has a "short" back-focus distance. The rear-most element on the lens is positioned farther back than a typical "EF" lens and actually protrudes into the camera body.
This is not a problem for any camera with an APS-C size sensor. Since sensor is smaller, the reflex mirror is also smaller. It doesn't require as much space. Since the EF-S lens protrudes slightly into the camera body, that mirror still has plenty of space to swing clear when you take a shot.
But when you try this on a full-frame camera such as 6D, 5D series, or 1D series, the sensor is larger and that means the reflex mirror also has to be larger. That mirror would hit the rear-most element of the lens when it tries to swing up -- that would be very bad!
To fix the problem, the entire lens really needs to be shimmed out forward a bit. Mounting a lens on an "extension tube" would actually work. But this creates TWO new problems.
#1 The lens is designed to rely on a 44mm distance from the lens mounting flange (where the lens mates to the front of the camera body) to the image sensor. If that distance changes, the lens focus will not work accurately. You could still focus, but may find that you have to focus manually ... auto-focus may be unreliable. When you use an extension tube, the entire focus range of the lens shifts closer and that means that the lens will no longer focus to infinity.
#2 EF-S lenses were designed as a cost-savings for APS-C size cameras. Since the sensor is physically smaller, the image circle projected into the camera body by the lens doesn't need to be as larger. So an EF-S lens actually projects a smaller circle. To do this requires less glass and it allows for a lens design that can produce a very high quality image at a lower price. But if you try to use such a lens on a full-frame camera you'll find that it can't produce an image that fills the frame all the way to the corners (well... it may be able to with a long enough extension tube, but see problem #1 above.)
This means you've got a mirror-collision problem and an inadequate image circle problem (causing severe vignetting around the edges of the frame.) And in trying to solve that problem it produces a focus distance and focus accuracy problem.
If you have a full-frame camera, make sure you get "EF" lenses. It's really not worthwhile trying to adapt "EF-S" lenses.
Without know exact model numbers most likely they will all fit & work. However the more modern versions will likely be a better lens due to faster auto focus or sharpness of the lens but what you have should be a good start at learning photography & where your interests go.
If memory serves me the 650D isn't that old. It is the other world version of the T3i (?) or T4i (?) or a close copy. Maybe 5 years old. I don't mess with APS-C anymore so I really don't know.
That should be the T4i. The way I remember it... is that the T1i was the 500D (I had a T1i so that one sticks in my head). Then add "50" for each generation... e.g. the T2i was the 550D, the T3i was the 600D, and the T4i is the 650D.