For the Stream Game Disc Image to Gamecube method, You need to have a crossover cable connection/router for this to work?
Yes. Either a crossover cable, to go straight from your PC to your GC, or a router and some standard patch cables, to go from your PC to your router, then to your GC.
Think for a moment and apply logic to your question. If you're using crossover cables, that's because you're connecting your PC directly to your gamecube's BBA. If you're connecting your PC directly to the BBA, where would you plug the second crossover cable into? If you're using a router, then you need to use a pair of standard ethernet cables(patch cables), because you connect your PC to your router, and your gamecube to your router through the BBA, which needs a cable to connect to the router.