Ok, I have international league pass broadband, so, I can't answer all your questions, but, here are the ones that I can answer for you.
1) I have a media centre PC hooked up straight to my TV at home, that is how I watch it. My friends hook their laptop via HDMI cable to their TV. I have a PS3, and that is not compatible with NBA League pass, I am not too sure about the Wii.
2) Typically, you can only be signed in to one device at a time. I learned this the hard way as my brother (whom I gave a login to) would log in, and kick me out in the process, to watch a game whilst I am watching a game, extremely frustrating.
3) This I am not too sure about, I don't record any of the games as all games are on demand, which leads to the last point:
4) Exactly, you can watch any game you want at any time. They give you approximately up to a month after the season is done to watch any game you want from the previous season.
Personally, I am from Australia, we get ESPN on cable, but, that is it. So, my only options is watch 2 x double headers per week, or getting the league pass. I love it, best money I have spent.
Hope this helps.