kext = Kernel EXTension, it's another name for drivers, i.e. it's part of the OS, not Chameleon which is "just" a boot loader (although it does help to inject parameters to the OS). Chameleon would not prevent a LAN or WLAN kext to load.
You can check your hardware specs with Terminal command lspci -nn and post us the output. In addition, list us the kext you have in /Extra/Extensions folder.
Yes, you can simply install/re-install Chameleon through myHack; it should still allow you to boot Win and, in theory, Linux (TMX bootloader is just a copy of Chameleon afterwards). You would normally find myHack in Applications folder, there's no need to reboot from your USB installer.