You may want to 'lock out' the suspension fork to give a stiffer ride. It'll give you a little more speeed and you'll feel the road more.
And yes, by all means roll the handlebars away from from you.
1)Loosen the pivot point on the stem and flatten the adjustable portion 'til it's parallel w/t ground.
2)Then loosen the handlebar and 'roll' it forward slightly...not too far or you'll have to re-adjust your shifters and brake levers...a whole 'nother kettle o' fish.
3)Then go to your saddle and loosen the rail grip bolts. Slide your saddle back about an inch. Make sure the saddle remains flat. If the saddle is angled down after sliding it back loosen the tilt mechanism and move the saddle until it's flat. Make sure there's enough height from the top of the saddle to the bottom of your crank arm circle so that when you're sitting on the saddle and the crank's all the way down you've got a slight bend in your knee. If when pedaling you have to 'rock' back and forth the saddle's too high. Lower it until the rocking motion stops.
Your problem looks like the bike may be a little too small for you. So, I'm trying to make suggestions based on what I see in the pics and what you stated in your text. At somepoint you may want to get a longer stem and a different saddle. The pictured saddle is designed for 2 mile, relaxed weekend rides on the MUP not 12 mi rt daily commuting. 240+ miles per month isn't chump change mileage.
You're pushing 3,000 miles per year just in commutation miles. Add in whatever you do on the weekends and suddenly one finds themselves understanding why some cyclists can seem a bit snobby about their gear.
Btw, welcome to BF and the wonderful world of commuting! Take everybody's advice w/a grain of salt, realize opinions and depth of experience vary quite a bit, but everybody's
at least helpful
PS: Your taillight looks like a Cygolit Hotshot. You may want to make it a perpendicular as possible to maximize it's effect.