There is a high chance he will exit the cave some time tonight (if not already). Basically, as of a few hours ago they only had the 350m entrance shaft to negotiate, which, compared to the rest of the cave is relatively straight forward. Plus, there is access to plenty of fresh manpower and the psychological effect of being so close is a big factor now too. And yes, there has been some speculation about closing the cave, but I think this is just media talk at the moment.
As for costs, the DAV (alpine Club) will cover search and rescue up to 25000 Euros, so that won't go far. I guess the cavers solidarity fund had several thousand Euros in it so that will be exhausted. The whip round as mentioned above will hopefully help too. Since there has never been such a major rescue operation as this before I can see that it may result in a complete review of the rescue system currently in place.