1. No. You best bet is the availability tool on KE site. If it has seats available for your flights/dates, then DL should have it. If not, call back until you get a better agent.
2. No, DL does not allow you to book first class on any airline, ever.
3. No. It has been like that for a year or so. Back to early 2011, though, you could select seats much further (don't remember how far, but was at least some 200 days) in advance. But, with the fleet upgrades, KE made it to just 30 days, likely due to only planning which aircraft will be on a route a month or so before.