PS+ subscription comes "on top" of the usual (free) PSN subscription, you're not restricted to playing with members of either group of users by being a member of one group or the other (PS4 games can only be played online if you're a PS+ subscriber, though).
The games offered through PS+ "Instant Game Collection" are exactly the same as their "full priced" counterparts, meaning they have all of their features intact, including online play. If you got a game for free through PS+, you'll be able to play it as long as your PS+ subscription still hasn't expired; If you bought it with a PS+ discount, it's yours to keep forever.
One exception worth noting with PS+ is that a couple of free games offered have only their "single player" component included. These are "Uncharted 3" & "Starhawk". The online component for these games can be bought separately.