Is there a way to set multiple focal lengths with one projector and software?
As shown in the following illustration, the image from one projector is partially in focus and partially out of focus.
Assuming that the screen output from the projector is viewed with the camera again, is there a way to correct the part out of focus with software?
No this is not doable by SW only.
Because you would need to change the direction of light coming out from the projector's emitter so that after passing the optics will focus further away and SW can affect only Color change...
What you need is to tweak the projector optics changing the focal length of lenses. You can do that by adding another lens in front of projector (with the right focal length in the right distance). My bet you need concave lens (negative focal length) however You need to make sure the cooling of the projector itself will not be affected so it must not reflect too much light back, and also take in mind this will most likely create some color focusing problems. I would simply test this with holding such a lens in hand and see what happens with the image focus while moveing it ... however I got quite a lot of lenses at my disposal which I assume most people do not have.
However you can test this in SW by using any optic lab SW or even write you own and simulate the projector there ... after obtaining the proper parameters for your new lens you can purchase it at any optics (where eye glasses are made/sold) unless the focal length is not too weird...
Another option is to tweak the projectors lens system which is most likely a teleobjective so if you can slightly tweak the distance range between the lens mechanically which could do the trick however the lens movement range usually corresponds to their diameters and apertures so its possible such change will cut of some parts of screen (on the outer borders). Also this usually means loss of warranty as you need to mess up with the device itself and also if not done properly you could damage the lenses for good so I do not advise to do this unless really necessary.