Could I use a male to male usb cable to connect the two, then be able to read and write files on the Airport's HDD?
Sorry, but no, since the USB port on the Time Capsule is there only to allow an additional hard drive to be connected to the Time Capsule for more storage, or to connect a compatible USB printer.
If not, then please tell me how to set it up through my network and not use it as a router
Connect an Ethernet cable from one of the LAN <--> ports on your main router to the WAN "O" port on the Time Capsule, set up the Time Capsule in Bridge Mode (which turns off the routing function of the Time Capsule) and then turn off the wireless function on the Time Capsule (to prevent the Time Capsule wireless from interfering with your network's wireless service.) Apple's setup "wizard" will do most of the work for you automatically. You will then use AirPort Utility to manually turn off the wireless on the Time Capsule as a final step.
As you might imagine, Apple will frown upon this type of setup, because they expect you to use the Time Capsule wireless.
Also, i did 2 factory resets and it would not let me "set up as hard drive" as some websites suggest
Not sure what websites you are referring to or what "it" might be, but the instructions above will do what you want.....to set up the Time Capsule as a network hard drive. If you are not familiar with Apple's set up "wizard", post back for more details. Here, I am assuming that your Mac is running a current or recent version of the operating system.
It would really help if you could provide the make and model number of your router, and what operating system the MacBook Air is running at the present time.
And I have a macbook air so I can't connect it via ethernet to my computer
The setup "wizard" assumes that you will be using WiFi to set up the Time Capsule, so an Ethernet connection is not required on your Mac.
