It would decrease the mutation rate per generation. Most mutations occur in men, as their germline cells replicate many more times than in females, and the mutation rate increases with age.
Just shortening the generation time would scale the x axis, yes. The simulations are done in terms of generations, and the years are just calculated at the end by multiplying.
A short generation time is implausible, though. In modern hunter-gatherer societies, puberty occurs around 15 and first birth about 2 years later, with late weaning and a relatively long time between births. This is the data that makes people think the typical generation time for our recent ancestors was 28 or 29 years. In chimpanzees, the mean generation time is ~25 years.
Such possibilities are often quite bounded by other data, though. Radiation contributes a very small fraction of current mutations, with cosmic radiation being a small fraction of that. Very large increases in radiation would increase the mutation rate, but radiation-induced mutations look very different from the genetic variation we actually see in humans.
The answer to the 2nd question is yes. The answer to the first is yes, but not easily. The mutation rate really isn't likely to change on short timescales, though. Most mutations are the result of internal biochemical processes, processes which are similar in similar species. As I pointed out earlier, different processes produce different mutations, and a change to one process (like radiation-induced mutation) will be evident.
In general, it seems reasonable to conclude that the creature that's quacking, waddling across my lawn, and looking like a duck is in fact a duck. While it is in principle possible that, thanks to a set of circumstances I haven't thought of yet, the creature is actually a turtle, at some point it becomes the responsibility of someone arguing, 'Hey, maybe it's a turtle', to provide some kind of evidence to that effect.
The bottom line is that human genetic variation looks exactly like the result of a long-term largish population plus recent expansion. It does not look at all like the result of a tight bottleneck. Simple pop gen reasoning says that such a bottleneck would leave easily detectable traces for hundreds of thousands of years. Simulations bear this out. Until someone can demonstrate that there actually exists a plausible model that would hide the bottleneck in that time frame, I don't see much point in pursuing the question further.
BTW, my immediate plan is to take at least a few days off from contentious issues on the internet, so I intend not to comment any more for a while. It's going to be nothing but Netflix and puppy videos for me.