Can the Canon MP-E 65mm lens be used with a Canon T3? Is an adapter needed? Is there another lens which might offer the equivalent Macro capabilities?
Yes, you may use the MP-E 65mm lens on a Canon T3. No, you do not need any adapters.
Just realize that the MP-E 65 is a different type of lens than what you are probably used to. Not only is it a manual focus only lens, but at each magnification setting there is only a single distance the lens is capable of focusing. The way most users focus is to set the magnification desired and then move the camera away from/towards the subject until it comes into focus. Having the camera tripod mounted is essential, and having focus rails between the tripod head and the camera is even better. The MP-E 65 also requires a lot of light to use, as the effective aperture at various zoom settings is narrower than the set aperture. Effective Aperture = (Aperture Setting) + (Aperture Setting x Magnification).
The MP-E 65mm 1-5X Macro lens is a unique piece of hardware with a steep learning curve and has very hard limits in what it can do. But within those limits it can do things no other lens can.