Rookie cyclist attempting to commute on 45 MPH posted roads with more like 50-55 MPH actual speeds during rush hour = "Are your life insurance premiums paid up and will you kindly name CampyBob as your beneficiary?"/
What's legal? Riding your bike and following all the traffic laws is legal. Using more than the required lighting, Hi-Vis clothing and all the cycling safety gear available is advisable. Aside from Americans being averse to exercise, there's a reason you don't see many cycle commuters...it's dangerous. And it takes preparation, planning and several skill sets not practiced by Mid-West urban dwellers.
I would advise you to get in touch with your local bike clubs, city bike commuter council or equivalent organizations, local representative of the League of American Bicyclist, etc. These folks can provide you with the knowledge that will make your commute survivable and possibly enjoyable. They know the safest routes and can educate to you as to what is required to arrive alive.
Provide more details as to the distance you intend to cover, the terrain type, your cycling experience level and other pertinent information and other members on the forum can fill you in with their commuting experiences.