Do all Canon DSLRs have in-body AF motors?

No Canon EOS body needs AF motors because every single Canon EF lens released since the EOS system was introduced since 1987 has a focus motor in the lens. Thus no Canon EOS camera has ever had a need for a focus motor in the body.

There are a few manual focus lenses in the EOS system, but they are clearly designated as such by not being named as an EF lens: The MP-E 65mm 1-5X Macro lens is one such example. The TS-E series of tilt & shift lenses are another. Beyond those few rare lenses every EOS lens has AF capability built into the lens. The vast majority of those lenses have Ring type UltraSonic Motors driving the focus mechanisms of those lenses. A few lenses have newer STM motors which are more suited for use capturing video. A few others use micro-USM motors and a few others use plain old geared motors to drive the AF system. But all of them have the AF motor located inside the lens.

Not only do Canon EOS bodies not need a clunky, noisy mechanical interface between the body and lens for autofocus, but they don't need a mechanical linkage prone to adjustment issues left over from the 1950s to control the lens' aperture either. This means that all communication between a Canon EOS body and a Canon EOS lens is communicated electronically.

No Canon EOS camera has an in-body focus motor. Canon's lens mount is 100% electric, there is no mechanical linkage. (Some mounts e.g. Pentax have a mechanical link for the aperture too, for some lenses).

The EF designation of Canon's lenses stands for Electro-Focus - in other words, the focus is driven electronically. Each lens has a built in motor.

There are some exceptions, most notably the MP-E and TS-E lenses are manual focus only. However, the aperture control is still electronic, hence the "E" in the name.

No. All Canon EF lenses have in-lens motors. There is no need for an in-body AF motor.

The Canon EF mount is designed to have no mechanical coupling of any kind—no aperture levers, "screw-drive" AF couplers, or any other mechanical linkage between the lens and body. It is entirely electronic; all EF lenses have autofocus motors and electromagnetic diaphragms built in.

Note that there a few EF-mount lenses (the tilt-shift lenses and a 5X super-macro lens) that are manual focus. Although they are electronically controlled nonetheless, the lenses themselves are not designated EF because they are not autofocus. The tilt-shift lenses are designated TS-E; the 5X super-macro lens is designated MP-E (macro photo).

Some fun facts about the EF mount and Canon EOS: The EF mount is, in fact, the first entirely electronic mount, having been introduced in 1987. Hence, Canon has the honor of having the world's first fully electronic camera system. So how do other systems stack up?

• Until very recently, all Nikon lenses had a mechanical aperture lever controlled by the camera body. Only those lenses designated with the letter E after the aperture specification have an electromagnetic diaphragm, and many lenses (primarily older designs) still rely on an in-body AF motor for autofocus.
• The same can be said for Pentax; electromagnetic diaphragms and the corresponding KAF₄ mount specification weren't introduced until June 2016 with the Pentax DA 55-300mm f/4.5-6.3 PLM lens. A large number of lenses, both old and new (though mostly cheaper ones) rely on the in-body AF motor for autofocus.
• As far as I know, Sony continues to rely on mechanical aperture control in the A system, and older lenses still use the in-body AF motor. The E mount, however, is entirely electronic.
• The Four Thirds SLR system and all major mirrorless systems, except for the Leica M rangefinder system, have fully electronic mounts, but they weren't introduced until well into the 2000s.