1. I do have free electricity, but the bw is quite limited, is it disadvantage in mining ?
2. If I can somehow get one of those ASIC thing, do I need a computer to plug it in or it will work out of the box like a rice cooker.
1.) In total, I don't think my miners use anymore then 10KB. I'm running mine on a 1Mbps line. As long as your latency (ping) is fine, you're good to go. If it's 1000+ms, you are likely to experience stale shares.
2.) Some of them need to be plugged in, some don't. It depends on which model you are looking to purchase.