Is there anything that can be done to improve and bring the small 1.6 engine to modern day gas mileage standards?
That would be so cool!!!!!!!!!!!!!!!!!
This may sound incredibly stupid but it really isn't:
Give it a thorough tune-up. If necessary, rebuild the engine and you'll get better gas mileage.
Also, and I speak from personal experience, take it easy with the skinny pedal!
Back to performance improvements...
If you have the money, I would suggest an aftermarket exhaust manifold and a two-inch exhaust system. It's not Zany-cheap (like that 10-cent resistor that GF Performance wants so badly to sell you for $65) but you'll actually notice a change.