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- Does the LDS church assert that doctrinal statements made by the current Prophet are either "inspired", "infallible", or both?
Inspired, definitely, but not infallible. Prophets are merely mortal men.
- Has the Prophet made any statements about (near)future events that Mormons expect to happen?
Yes, actually. Just a couple months ago, President Monson announced that four new temples would be built in the near future, and named the cities they will be built in.