You might not get excited about it, but sponsorship runs deep through F1; the teams getting to the top are the ones with the best funding, which comes from various sources but is driven by sponsorship. Some sponsors pay for space, others actually work with the teams on making the car go better. A car that goes better gets better results, hence is seen on the TV more, resplendent in all its decals. Happy team, happy sponsors.
Oil and fuel can actually affect how well the car goes. Or not - see what happened to Lewis last year when the oil specification got a bit too close to the edge. It cost him the championship.