Have you read Alexman's "Everything about Corruption: C3C edition"?
That tells you almost everything you need to know. Then I'd recommend getting some paper and sketching some empires so you get a feel for how the distance and "rank" elements interact.
As for your specific questions:
1. Ring City Placement (RCP) was a bug-exploit that has been fixed in final patch C3C. The idea was that when calculating ranks, the game treated all cities with the same distance as having the same rank. Add up distance: 1 across a tile border (NE, NW, SE, SW), 1.5 across a tile corner (N, S, E, W). So if your empire consisted of a capital and then 12 cities all placed at distance=10, all 12 would have rank=1 (capital has rank=0), instead of rank=1, 2, 3, ... 12. That was HUGE because all 12 cities would have almost non-existant rank corruption (under 3%), even though they should have been far higher.
As I said, this was fixed. Now, each city gets its own rank. If distance is the same, the game has a few tie breakers to use (e.g., date of founding).
Now, however, players still talk about "rings" because when you place your cities, you should place them at roughly uniform distances apart, based on yo9ur strategy: warmongers and ICSers like close spacing 3-4 squares; builders usually prefer 4.5-5.5 squares (using the distance calc explained above). In either case, your empire will consist of several rings of cities around your capital, the first at 3-5 tiles away and including 4-6 cities. The second is the same distance again, and might have (if coastlines or neighbors don't get in the way) 8-12 cities. You get the idea...
Your cities don't HAVE to be in rings; they just end up that way for most players.
2. Saying that that FP should go in a second ring or third ring city just means that however close you are building your cities together, put, the FP in a city in the second or third ring out. That might be 8-15 tiles away from the capital.
For more, see some of my comments in the recent threads on this topic:
http://forums.civfanatics.com/showthread.php?t=116691
http://forums.civfanatics.com/showpost.php?p=2623616&postcount=17
http://forums.civfanatics.com/showpost.php?p=2646635&postcount=9
