The internet backbone is the exchange of traffic between tier1 and tier 2 networks(mainly ISPs). Tier 1 networks are IP transit providers that sells to smaller ISP. The term "backbone" is practically a collection of WAN networks that operates on the "internet". As of today there are only a few IP transit providers or tier 1 networks. The most important thing to remember is the "internet" is a network of networks that is decentralized, meaning no particular organization has the capacity to manipulate traffic.
1.What is the tier structure of internet connections (the physical trunk lines) ?
-ISPs connect to other ISPs in a number of ways. The most common is smaller ISPs buy IP transit from Tier1 networks to establish connection or they could also connect to an IPX (Internet exchange point) to exchange traffic from other ISPs
2.Which companies/organizations/governments provide the most basic/core lines?
-Tier 1 networks http://en.wikipedia.org/wiki/Tier_1_network
- At which level do local ISPs figure? (The company that gives me internet)
-There are called regional ISPs, It depends how scalable their infrastructure is. Most Tier1 networks exchange traffic through a process called "peering", meaning they get to connect to other tier1 networks for free.
4.What is the tier/level of the providers that connect data centers to the rest of the internet?
-Data centers establish their connection to the internet through a tier1, tier2 or tier3 provider.
- How do companies charge each other for routing packets over each others networks? Do they even charge for this?
-Tier2 and Tier3 network purchase IP transit, only Tier1 networks get to "Peer".