Here's one important detail that will answer a lot of your questions, Apple iDevices will draw no more than 12 watts from a USB-A port. Another important point, Apple iDevices use USB-PD (power delivery) to get more than 12 watts from any USB-C power brick or dock. Quick Charge and PowerIQ power bricks will not work unless they explicitly state they are USB-PD compatible.
It doesn't matter what the power rating of the power supply is, an Apple iDevice will draw no more than 12 watts from a USB-A port. If there is a USB-A connection anywhere in the chain from the wall outlet to the Apple device then the power will be limited to 12 watts. That Anker 60 watt USB power brick? That's 60 watts because it's 5 ports times 12 watts per USB-A port.
Some non-Apple devices will allow more than 12 watts per USB-A port, such as Quick Charge and PowerIQ. They do this by putting a protocol other than USB-PD over the USB port. Apple iDevices will not "talk" anything other than USB-PD to negotiate power draw and so will fall back to a kind of "safe mode" of 5 watts maximum that dates back to the days of USB 1.1.
I want to hammer this point home because it seems people here are missing this important point and it's causing them to waste a lot of time (and possibly money) on trying to get more than 12 watts through USB-A. It won't happen. Or it should not because if it does happen then something is on fire or is about to be.
To get more than a 12 watt trickle into your Apple iDevice (laptop, tablet, or phone) it needs to connect to a hub, dock, or power brick by USB-C or Lightning. If there is a USB-A connector at any point between the wall outlet and the Apple device then charging will be limited to 12 watts, possibly 5 watts. If there is a hub, dock, or other device between the wall outlet and the power input port on your Apple device then it needs to get power from something other than USB-A. Most often this will be a USB-C power brick but some docks will use something like a barrel connector or 4-pin DC input, something capable of handling enough power for the dock with enough left over to charge the Apple device, then the connection to the iDevice will be USB-C or Lightning.
Seeing a dock consume 7 or 11 watts sounds a bit high but if there's other devices plugged in other than the iDevice then that would explain the power draw. I have used a 27 watt USB-C power supply to keep my MacBook Pro powered before. My dock will consume 2 watts of that for the dock itself and the keyboard and mouse attached to it.
If the power supply is not powerful enough to power the dock and meet the power draw of the iDevice at the time then there will be nothing left over to charge the battery. In which case you should get a more powerful power supply that uses USB-C and USB-PD.
To complicate things further the cables can be the weak link. There are 3 amp USB-C/USB-PD cables and 5 amp USB-C/USB-PD cables. You need not be concerned about that unless you need or want more than 60 watts.