Neuroscience - Brain scan a person from all religions to show it's the same thing that they are all doing. (massive blood flow reduction in the part of the brain that orientates their positioning)
Eco - Do a tidal power generator crossed with a desalination plant. Experiment with resonance frequencies of hydrogen and ionosphere for clean power. Make ultra cheap solar panels and dump them in the desert. (pretty sure some tin foil, a way of converting and some genetic algorithm shaping should get this done) Patch any ozone holes with spraying of o^3 / something to counter act the cfcs. Co2 problem (down to 60% of the problem from 90% a few years ago) harvest the co2 out!
Physics - There's always going to be smaller! One of the strings in string theory is consciousness
Society - Legalise all drugs, prostitution and assisted suicide (stops making so many people into criminals) No speed limit on motorways at certain times
Biology - Find what plants grow well in all soil / sand conditions. (grow the desert / useless land) Bacterial recycling / break down of rubbish.
TV/entertainment - Providers release torrents / streams to anywhere with ads before the pirates do it for them.
And to answer the ops questions: 1. I think it's possible to influence fields you have no expertise in, as can email scientists / producers. 2. yes 3. More empowerment to people to get involved. One day a year ask people if they have any ideas or suggestions in x field.