Strictly speaking, if you actually traveled at the speed of light, the trip would be instantaneous from the reference frame of the craft making the trip. It would still take 111 years from our frame of reference on Earth.
Also assuming no acceleration or deceleration time in this made up impossible scenario. In the more likely scenario where we can get to a fraction of the speed of light using current technology we do have to account for both factors in both time and space probe weight.
Yes, but we can't actually travel there with our current technology, and while you're speculating about future technology, you can pick the number of 9's to tack on to your cruise speed pretty much arbitrarily. So from the probe's perspective, it takes somewhere between a fraction of a second and many billions of years to arrive.
