Up to you. I've had long runs with nothing to eat before and nothing to dring during (camelback broke) and survived, but I had something to eat afterwards. That said, if it is C25K you should be fine.

It might not kill you, but I would certainly be extremely unhappy to run without having had water for a while and not being able to have water for several more hours.

Besides which, and I mean this with all respect, if you're trying to get a run in, you're missing the point of the fasting in the first place. The symbolism of Yom Kippur, besides the idea of fasting for repentance, is that we are supposed to behave as if we are DEAD and being judged. The dead do not eat, drink, or have any comforts (bathing, perfume, leather shoes), and they certainly don't run. What is the purpose of your fast if it's not going to lead you to the spiritual dimension of the holy day and it's just another day to squeeze in a run?

I'm fasting as part of Ramadan from pre-dawn to sunset and I've kept running. I've kept the runs to 45 minutes so far and haven't had any problems. The first run was after not having eaten for almost 24 hours (I ran just before dinner, not having eaten in the morning) and I felt fine. It takes experience to be able to do it, but it seems as though your workouts are short enough to be manageable.

I have run as long as nine miles while fasting and it seems to work best to run right before you break your fast, for obvious reasons. I would run in the morning but I never do that as it is and I think I'd be hurting myself by going without food and water for 8-10 hours. Again, with shorter/easier runs it's not an issue, but it is when you do hard workouts.

Any training program worth its salt has some wiggle room in it for injuries, "off" days, or scheduling conflicts. You should be able to either switch days around or even skip a training day or two with no adverse effects on your long term goal.

That being said, I actually took a survey at our local RRCA club meeting last night and none of them are running on Yom Kippur, although they thought that it wouldn't hurt them, as long as they ran close to the end of the fast. 24-25.5 hours is a long time without food or water, water being the most important thing here. Just be careful and tell someone when and where you're running in case you don't fare well.

I'll be thinking of you as I sit in shul, sitting and standing and sitting and standing and sitting and standing...

Good luck