Looking at, https://learningnetwork.cisco.com/docs/DOC-5278, the 2960 will be a 2960 (not 2960S) with a version of the 12.2SE LAN Base image. It will probably have PoE to support an AP. As for the 3560, it is a 3560-E switch (again, in the same document,) probably with PoE as well. Don't get too hung up on the exact model of switch (outside of the generalities listed in the CCIEW Equipment List.) As for the exact version of software on the switches, again, don't get too hung up. Generally, the features are taken from the base image. Then, if bugs are found that impact the lab, switches are upgraded to correct the bugs. They are not upgraded to add features (based at what was shared during Cisco Live at one of the CCIE Techtorials.)
As for the 2106 power supply, that is AIR-PWR-2106-AC=. The "=" is part of the official Cisco part number. You can find it other places without it.