1) the later of 2 years from the offering date or 1 year from the purchase date. Most plans are 6 month single purchase offerings and therefore it ends up that the 2 years from the offering date is the applicable period which would be 1.5 years from obtaining the shares.
2) Many (most?) Will say to sell right away and reinvest in the general market as you stated. But if you have enough risk tolerance or other diversity, the tax benefits are great. You don't have to keep or sell them all, you can keep just enough for DIK. I sold most of mine with my current company because it was very up and down. Looking back I probably would have kept the first 1 or 2 purchases before I started selling them so Id always have some in LT status. But it's easy to look back and say that. Your advice is probably best for most people and those with low tolerance for risk.