You need a WiFi router or access point. For instances an Airport will do what you need.
you need to connect your ipad to itunes on your windows 7 pc via the USB cable one last time, so you can enable wifi syncing for the ipad within itunes. Once you do this all subsequent syncing can be done over wifi.
I was having trouble with this earlier today. Both devices must be connected wirelessly to the same network. My iDevices and MacBook weren't finding each other, and then I realised it was because my MacBook was connected to my router's 5GHz network and the others were on the 2.4GHz.
Nope. They don't both have to be connected wirelessly.
OP, I don't really know what the problem. I would mess around with your router settings a little bit.
Wireless has to be switched on the PC and connected to the same network as the iPad, regardless of whether you use wired to connect the PC to the network.
Neil.