1) You can give armours to soldiers either through the "equip craft" window (where you can do it even to soldiers not assigned to a craft) or through the soldiers entries (but that interface is not so great), before the mission happens. You can do it right as you see the battleship coming in. Unfortunately, once the base defence mission starts, it's already too late. All your guys have time to do is grab a weapon!
2) The behaviour of all UFOs is scripted, so a UFO on a given mission will always behave in the same way. What changes is the regions where they perform specific actions. They will spawn in random regions, fly to their mission specific region, perform their mission, fly to a random region and go away.
If you know the mission (using a hyperwave decoder), you can predict if they will land or not. If you don't know the mission, then you take your chances (or, like me, you don't and shoot the buggers out of our sky. I'd rather have no Elerium than let some aliens get away!). The first mission of every game is a Sectoid Alien Research mission in your starting region, which I think involves landing for most of the UFOs, so that's a safe one. After that, good luck!
3) I suppose you're using the "psi-training any time" option? That one is actually rather clunky and gives no report. I have been using it but I think I like the monthly training (and reports!) better. Otherwise, checking often is the best I could do..
