Yes it has an image stablizer built into it.

The Canon EF-S lens is compatible with the AE-1, as well as most of the other Canon SLRs.

It depends on what you want to photograph, assuming you need this and not just "view" (that's what binoculars are for). I suggest a 200mm telephoto as a minimum, ideally 400mm. As price increases considerably, you can use an adaptor to increase focal length. A 2x adaptor will provide 400mm instead of 200mm, but you will lose on quality. Also, considering the distance, you will need a tripod to shoot steadily at such a distance. Some telephotos will have stabilization (VR, IS etc depending on manufacturer) but best results will be provided using a tripod.

The focal length of a camera's lens refers to the the magnification or telephoto power of the lens and is expressed in the millimeters of the lens, like 100mm, 300mm, etc.

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The Canon Rebel film bodies use the EF mount lenses. All modern Canon EOS cameras, including all digital EOS cameras will also accept EF mount lense.

The EF and EF-S lenses are compatible with the Rebel series. However, the lenses that typically come with a Rebel (EF-S) are compatible only with Canon cameras that have a 1.6 crop factor. Cameras with the 1.3 or no crop feature will not accept the EF-S lenses. The lens mounts deeper than the mirror will tolerate.