So it sounds like your problem is solved, right?
Just to address some of the questions and observations:
The ethernet (wired) connection speed is independent of the wifi link speeds (at a physical level). So, no, the wireless devices don't also necessarily drop down to 100Mbps link speeds.
Obviously a 100Mbps connection from the AP to the upstream infrastructure limits the speed of actual data transfers from the (clients of the) AP to upstream devices, but the wifi link itself could still be established at a faster rate. You can think of it the same way as your home network functions -- you can have a gigabit copper link between all of your devices but only a 100Mbps or slower link to your ISP and things still work just fine (just a limit of 100Mpbs to the internet).
This seems not to be the issue in this case, but don't automatically assume that brand new cables are always good. They can be faulty -- including intermittent issues. For example, if one of the ends isn't crimped quite right, you could have an intermittent connection between one or more of the pins and the wires. This could be affected by movement or even just temperature (which might fluctuate due to time of day, heat/AC, surrounding equipment, sunlight hitting it, etc.). When in doubt, cables are a simple thing to swap out as basic troubleshooting, especially if you're getting a lot of port-flapping or drops in negotiated speed.
I'm a little confused about this, but it sounds like things are working properly now? This could indicate an issue with the physical port (i.e. debris in the connector or some other mechanical issue; an electrical issue with the circuitry, or an issue with the software driver in some circumstances).
Another thing to keep in mind is that the colors for the indicators are not always standardized, nor are the meanings of a given LED. For example, a flashing amber LED on the front of an Apple Airport/Time Capsule device actually means that there is something that needs attention (such as a firmware update, or an issue with the upstream connection), while solid green means everything is okay -- it doesn't represent the connection speed, though. Some devices have 2 LEDs to indicate port status (10/100 = left, 1000 = both), some use different colors, etc. So just make sure that you're correctly interpreting what it is trying to tell you. But, it does sound like everything is fine now.
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