how does it work? does the roster change every month? do they tell you in advance which games are leaving the collection? say, a game exits while I'm downloading it. do i still get it? do you have to have finishe downloading the game for it to count? or once you've "purchased" the game, it's yours?
The Instant Game Collection roster changes mostly weekly now. At least that's been the tempo for the program as of late. The games that are excused from the lineup will appear in the expiration folder on the store, while new games are announced every Monday on the PlayStation Blog to appear before the Tuesday update.
If you've happened to download a game at the last minute before it gets cancelled, then it still counts. All you'd need to do is download a game and have it on file in your download list for it to be yours through what you've acquired through Plus. "Purchasing" a game is when you buy it. When a game is free, like the ones in the Instant Game Collection, then all you'd need to do is just add them to your cart and hit the download button to begin.
As for as the "finish downloading" part goes, your best best is to "purchase" all of the free items each week. As long as you "purchase" them (i.e. complete the check out process for $0.00 spent) the games will be available for you to download at a later date, as long as your PS+ subscription is active.
I don't think Sony (US PS+ program) does enough to give us advance notice of what is coming and what is leaving. For example, we all know something new is coming for Vita next week, however without knowing what the title will be (retail Vita, PSN Vita, retail PSP, PSN PSP, PSOne) I'm holding off on any purchases until an announcement is made. Disadvantage Sony; I have plenty in my backlog to hold me over.