Question for those that have been to World Cup before

I have a friend in the State Department stationed in Moscow. My family (wife, kids that will be 11, 7 and 4 at the time of travelling) are planning on visiting him and his family next summer in Moscow and then head off to St. Petersburg.

Not thinking about the World Cup, we scheduled with him to go in late June because his tour is up sometime in July. Not wanting to fight the crowds, reduce the price gouging and not wanting to expose my kids to soccer hooligans while the World Cup is going on, we altered the plan to head to Russia in late May and leaving the first week of June (about 10 days before the kick off). The only other option is visiting him next easter vacation which would be approximately March 28th through April 10th and we have nixed this due to it being on the cold side and dark side.

A couple of questions
1) when do teams start arriving for in country training?
2) where could one find out where WC teams training facilities be?
3) when do fans start arriving? (assuming some dedicate fans come in to watch the training?)
4) any idea on the price mark up on hotels, etc in those weeks because of point 1-3 would be greatly appreciated.
5) when does the WC draw for pods occur?

any insight would be greatly appreciated.