How do I increase my average speed?
First of all I’d fix the saddle position. A low saddle will decrease your power output and can cause knee problems. As a rule of thumb your leg should be fully extended with your heel on the pedal in the 6 o'clock position.
Keeping the handlebars low or even lowering them further will generally improve your aerodynamics.
Make sure the tires are inflated to a relatively high pressure (depending on your weight and road surface, probably around 4–5bars) to reduce rolling resistance. Make sure the chain is lubed properly to reduce friction.
Wear tight fitting clothes to improve aerodynamics.
Regarding turns: Here I disagree with Adam Rice, a lot of turns will certainly decrease your average speed, especially if you have to brake. Good brakes and technique can allow you to brake stronger and therefore later, thus improving your average speed.
Since it sounds like you are using average speed as a benchmark of fitness or power: It’s relatively useless for that, even if you only use it to measure your own progress. Even on the same roads different wind or traffic conditions can cause a lot of variation.