1. Why was it revealed? The balloon was spotted by civilians who posted video and there was a temporary closure of an airport. It's existence became public knowledge (though not the country of origin). This is apparently not the first time this has happened, just the first time it came to public attention.
2+3+4. Why let it continue to fly and gather intelligence? My guess is that we lack the capability to reliably shoot down a balloon at 85,000 feet. There is probably not enough heat signature or radar return for an air-to-air missile and it is probably above the service ceiling for an interceptor to engage it with guns. Rather than try and fail, we say we could but we don't want to.
5. Why would China float such a conspicuous object over our nation? Because they can. We used (and probably continue to use) aerial reconnaissance over the Soviet Union, China, North Korea, Cuba, etc. because they could not easily shoot down those planes and drones. The aircraft were conspicuous and the targets of the reconnaissance knew we were overflying them. Why wouldn't China do the same?
What benefit does a balloon have for reconnaissance over a satellite? It's closer, so imagery and electronic surveillance can be better. It is loitering over the area at 25 km (much closer than the 35,000 km of a geosynchronous satellite).
In case you are wondering how a balloon can loiter over an area, take a look at the work Google did for Project Loon. They determined that winds at different altitudes had dramatically different directions and speeds, and by ascending and descending they could control the area the balloon stayed in.