Some layer-2 protocols use MAC addresses, and some don't. For example, PPP uses something different. Your router will encapsulate in the layer-2 protocol which is used on the link to the ISP, and that link may or may not use MAC addresses.
Unless you work for the ISP you can't know what a particular ISP does internally because there are many different ways that ISPs do things.
Resource recommendations are off-topic, so we can't help with reading resources.
When you say error control, I think you are referring to error detection and correction. There are theoretical protocols and real-world protocols.
In the real world (in the vast majority of networks you will encounter in 2018), the dominant data-link protocols are Ethernet (802.3) and Wi-Fi (802.11). There are still other WAN protocols used by large carriers, such as PoS, but their use is waning.
Neither Ethernet nor WiFi have any error control, other than discarding corrupted frames (as @ronmaupin points out). If a frame is corrupted, it is simply dropped with no notification to the sender or receiver. It is up to higher level protocols to perform any error recovery.
There are (or should I say were) some DL protocols that did do error detection, such as X.25, but these are essentially obsolete. As the reliability of networks has improved, they are no longer needed. I haven't seen them in over 20 years.
But for all protocols, the layers are independent. DL protocols don't know what upper level protocols they are carrying, and upper level (like TCP) have no info on how the segments are transported.
Best Answer
Link layer Error Detection: A method to verify the integrity of frames when they are transmited over the media. The receiving side can verify if the received frame has been damaged on transit. If link layer detects a damaged frame, then it discards the frame and could or not ask for a retransmission. (Ethernet never asks for retransmission, it simply discards).
Transport layer Error Control: The sending side send segments that are divided on multiple packets at network layer and each packet on multiple frames at link level.
Each segment travels the network (divided as frames and packets) and is recomposed only at the receiving side.
Between the sending and receiving side could be a lot of intermediate routers. During that transit there could be problems as:
These problems will pass undetected through the routers until they get to the error control of the transport layer on the receiving side.
This error control verifies that there wasn't problems on the underneath layers problems and asks for retransmission.
Summary: As most of the errors happen on the media, not on network layer (routers, for example) there is a little redundancy, however only Transport layer is under the obligation of asking for retransmission.