1. Are you flying into KIX? If so, it should take about 3 hours by train. Take the Haruka train to Shin Osaka station and then the Shinkansen to Hiroshima. Cost will be about 12,000 yen if you buy ordinary tickets rather than using a pass of some kind.

If, in fact, you're planning to connect in Tokyo onto a domestic flight to ITM, you should consider flying to HIJ instead.

2. It depends how much travel you want to do and what level of luxury you want in meals and accommodation. You could get away with spending less than $50 per day if you're very frugal - staying in hostels, eating cheaply and getting around mostly on foot - but more likely to spend two to three times that amount.

3. I recommend that you get a guidebook or look at some websites like JNTO or wikitravel.