I believe you need to download Zune to your computer to transfer music to your Kin. But it's a free download and works like Windows Media Player or iTunes. Simply install the free software, connect your Kin, and drag your files down the the Kin icon in the bottom left corner. The Zune Pass feature is what costs money, after the 14-day trial period, and that is a subscription to streaming music, but you don't have to get that to put music on your device.
From the Kin devices I've seen, you will see both a 3G icon and Wi-Fi icon in the status bar, if Wi-Fi is on, of course. I'm not sure how to tell which you're using; however, you can block data through Verizon, or you can put your Kin into airplane mode, which means it won't use cellular data, but you also won't receive calls or texts while in airplane mode.
The only app on the Kin that would update would be your email, and you can set that to manually check.