First, are you sure that the covering is canvas? American Trader often covered canoes with fiberglass, and some of your pics show a fabric weave that could be glass. Properly filled canvas is generally very smooth, with the filler effectively hiding the texture/weave of the canvas. And canvas generally has a finer texture than the covering that is visible through the paint. On a canvas-covered hull. I would not expect to see the fabric texture that is clearly visible in the two photos of white paint with the bright reflections, and even visible in the photo of the green bulls-eye damage.
If it does not leak (only one way to find out), you might get away with paddling it as is -- but those cracks will eventually leak, and you will be better off if you deal with them now -- they are not like a skinned knee that will heal -- these cracks will only get worse.
Whether glass or canvas, you should not need a new covering. I will leave it to others to discuss how to deal with the cracks if it the covering is fiberglass.
But if it is traditional paint on filled canvas, you should be able to fix things up pretty well. You could try to deal just with the cracked areas, but that would mean trying to match paint color, something that is usually not a complete success. Painting the whole canoe, once the cracks are dealt with, is actually a fairly fast and easy job -- you can sand and smooth a hull exterior in less than a morning.
Now, as to the cracks -- and these comments only apply to a canvas covering that has been filled with a traditional filler:
At least two of the cracked areas seem to be the result of impacts -- the bulls-eye crack in the green paint, and the "S" shaped cracked area in the white paint with much red showing through. The other cracks may also be the result of impact, or they may be the result of the paint drying out over "many years" of storage.
Whatever the cause, the treatment is much the same, but long-term success is more likely with impact cracks -- if cracks are the result of drying out, more are likely to appear and the existing ones may re-appear.
Especially where paint has chipped away, sand to feather the edges of the chipped area, and similarly, sand the edges of cracks to eliminate sharp edges of cracks. This may be difficult on this hull because of the overall fabric has not been filled to the point of smoothness, and you do not want to sand into the canvas.
Once you have sanded as smooth as you can, you have two choices. On canvas that has been traditionally filled to a smooth surface, I would apply a spot putty such as Bondo spot putty (comes in a tube at auto shops -- not the two-part Bondo used to repair dents). One or two applications, sanding after drying, will give you a fair surface that can then be painted and the repair could be invisible.
But on your hull, where the texture of the fabric clearly shows., the repaired smooth areas filled with the spot putty will be noticeably smoother than the adjoining unrepaired areas. So, alternatively, you might want to skip the spot putty, and just apply a couple of coats of primer and paint. This might leave visible vestiges of the cracks, but the new primer/paint will actually seal things enough that there should be no leaking. Then paint the entire hull with the color(s) that you like -- the 2-tone green/white is very nice, but if you would prefer something else, this would be a good time and you should feel free to go with what you like. As to what paint to use -- some folks use top grade marine enamels -- expensive, durable, and great if what you want is a high-gloss finish. Other folks use Rustoleum, or a good porch and deck paint (Benjamin Moore or other good grade paint). Note that a semi-gloss paint will tend to hide any paint-job defects, while a high-gloss paint will tend to highlight them -- given what you are dealing with, I would go the semi-gloss route.
In any event, you will not have a hull that will pass a concourse d'elegance inspection, but should pass the 20 foot test -- "looks pretty good from 20 feet away."
And you should be able to get quite a few years of service from your very nice canoe.