We'll recommend a lot of stuff but the reality is, you're just about set with what you have.

You really should carry a spare tube, patch kit and levers and pump on the commute. That's it for essentials - you can commute that distance comfortably and safely with no other equipment. People will likely say that you must have lights, a mirror is mandatory, you really need to have fenders and so on. But none of that is strictly true - there are a lot of people who ride a lot of commuting miles without. Different strokes; I say jump in with what you have then decide for yourself what you really need.

In my personal opinion, lights are advisable, a rack is very convenient (tho I don't have one on my main ride), and I do like my mirror

You can carry an Ultrafire led flashlight if you want something inexpensive that you won't use constantly, or I recommend one of the MS clones under $20 on Amazon for more serious lighting. I see no point in spending more on lights for primarily daytime riding.