I read that the canon 35mm f/2 IS is the lowest aperture lens that also has IS. Is this because a stabilizer at any lower F-stop is not possible, or just because it is just currently outside of our practical technological capabilities? Also, I have noticed longer lenses typically tend to have higher F-stops, for example there typically aren't any telephoto lenses with an F Stop lower than 2.8 (although I haven't explicitly researched this). Is this because it is not possible to make it any lower, or because it is currently too hard to make such a lens with given resources and technology? I would also like to ask the same question with regards to wide angle lenses, the widest I know of to be an 11mm lens. How much wider could it possibly be pushed without being a fish eye lens?
There are several questions mashed up here, most of them based on false assumptions.
Rectilinear lenses and fisheye lenses are different and they can have focal-lengths that overlap. As in, there is an 11mm rectilinear but a 15mm fisheye. One does not simply switch below a certain focal. A rectilinear lens has a practical limit though since one cannot have it project 180 degrees, how close it can get to 180 is a matter of cost and design. One on the other hand fisheye lenses can view up 220 degrees wide at least.
A quick search on my site shows there are currently 31 telephoto lenses with F/2 maximum aperture. So telephoto lenses can have brighter than F/2.8 aperture. Remember that the aperture is a ratio of focal-length, so the longer the lens, the wider it has to be for having the same aperture. This makes brighter aperture telephoto lenses more bulky, so if you look at 200mm with F/2 aperture, there are only 3 and they all weigh at least 2.5kg (5 lbs).
Regarding stabilization, there are 17 stabilized lenses with F/1.2 to F/2 maximum aperture, so it is possible even for F/1.2 lenses to be stabilized. It is not a technology limit but an issue of lesser need. The brighter the lens, the more light it lets in, so stabilization becomes less important.