Q1 Yes

Q2 When used on an Canon APS-c sensor the lens has the same field of view as an 136mm lens on would have on a full frame body. The focal length is an intrinsic property of a lens and so doesn't change when mounted on a different camera. However most people use focal length [incorrectly] as a measure of field of view.

Q3 There are pros and cons to mounting the lens of an APS-c body. An 85mm lens on an APS-c body will be more prone to flare than a 136mm lens on a full frame body (the reason for this is that a lightsource that is out of frame on a crop body will still be in the FF frame and so light will not be occluded and can cause flare). You would also assume a lens designed for a crop sensor would be sharper as for the same number of megapixels smaller sensors will have higher pixel densities. This is not a hard and fast rule however. Finally using the lens on a crop sensor will avoid the extreme corners where a lens will often vignette or lose sharpness. The Sigma 85 f/1.4 is quite long but also very fast so will probably display soft corners wide open.

Q4 The lens will autofocus on the 60D (and all Canon EOS bodies).