The demarcation point is connected to the CPE (Customer Premise Equipment)
The CPE can be owned by or leased to the client.
Is CPE the modem and CSU/DSU? Or is it the router connected to the CSU/DSU?
The CPE is everything the customer owns. Sometimes the CSU/DSU is owned by the service provider, but sometimes it's owned by the customer. Same thing applies to the router. If the customer owns it, then it's the CPE. We often refer to the CPE to help determine who has responsibility to access and/or repair a device.
The connection from the CPE to the Demarcation point is the Demarc extension.
This isn't entirely correct. You don't generally have to extend the demarc unless you have the demarc in a distant part of the building, but your equipment is in another (this is quite common). The demarc enters the building in one central place, and then you use a demarc extension to move your circuit closer to the equipment.
What if the WIC in the router has the CSU\DSU? IS the router the DTE and the WIC the DCE? Does the service provider provides you with the WIC or do you have to buy it? does the service provider gives you the information to configure the WIC or does it configure the WIC for you?
A WIC generally refers to a specific interface that includes both a CSU/DSU and a WAN serial connection, all in one interface card. The software of the devices allows you to configure the features independently. If you own the CSU/DSU, then you generally have to coordinate with the service provider to determine the right configuration. Or spend time doing trial and error to match the configurations on both sides.
What is POP (Point of presence)?
The POP is the service provider location where your WAN circuit connects. Your circuit is usually a single path to the POP, so it's particularly sensitive to downtime should someone cut the cable. It's common to provide redundant links out of a building to different POPs (and perhaps even different providers) for redundancy and to maintain uptime.
Is it possible to use DSL or Cable to connect sites without using the internet?
It's entirely possible for a service provider to create a private DSL or Cable network, but there's not really a need for such a product. DSL is DSL, regardless of where it ultimately connects. I don't personally know of any provider that is using DSL or cable for private WAN connections.
When you want to have a frame relay connection, how do you ask your ISP for it? Do you say you want a T1 line and you are going to use Frame Relay over it? Can you use frame relay over anything else?
You can technically use Frame Relay over many WAN technologies. Frame Relay is an older technology that's not often seen in new deployments.
again, can you use anything else to run ATM over it?
ATM was a very flexible architecture that ran over almost everything. During the hype, it was promoted over many different medium. You don't see ATM much anymore.
It seems that T1 and Sonet deal with the physical layer of the OSI model and HDLC,PPP, ATM and Frame Relay deal with layer 2 of the OSI model.
If that is the case, can you run HDLC, PPP, ATM and frame relay into either SONET or T1 connections?
Technically yes, although it's not generally as mix-and-match as you describe it. Just because it's technically possible doesn't mean that your CSU/DSU, router, or provider support the combination.