The Ethereum network will be undergoing a scheduled upgrade at block number 7,080,000, which is predicted to occur on Wednesday, January 16, 2019. The exact date is subject to change depending on block times between now and then and could be activated 1-2 days before or after. A countdown timer...
I think you're referring to the original Casper FFG spec, which was cancelled 6 months ago. It never made "every Nth block mined by PoS" though. It just added finalization to existing PoW blocks based on validator votes
Ehh, unlikely that phase 0 will be that late. Phase 0 is just the beacon chain, so it won't have any increased throughput with sharding or any real security guarantees since the mainnet will still be PoW
Casper is the Proof of Stake algorithm Ethereum will use. It's to lower the energy footprint of ethereum, give better security guarantees, lower issuance, and increase decentralization, among other benefits