For NZ sites, you can usually expect to get speeds of up to 400Kbps during off-peak times and up to 128 kbps during peak times internationally. Obviously this is also site dependant i.e. a busy overseas site may not give you high speeds no matter how fast your connection is due to the load on their network. The dish is typically fixed in place and unable to tune to different satellites.
Sky is actually on a completely different satellite.
But you will only be able to access one of them at a time. Yes, any modem will work. The upstream traffic, which is mostly made up of download requests, only consumes a very small amount of bandwidth. A slow modem will work, but we recommend a 33.6 modem for best results. Satnet now comes in two flavours.