Paul,

Your first question is a toughie, individual performance may vary, but if you can comfortably put down a 15 - 20 mile ride now, knocking out two 13 milers shouldn't be a problem.

To answer question # 2, certainly your bike, if properly maintained is good enough. If you don't feel confident in bicycle mechanics (if true, you will need to learn to repair your bike and carry some basic tools and parts), have the LBS do a tune up to provide some inexpensive insurance. The last thing you want on a commute is a breakdown to cause you to be late or miss work. Good high pressure street tires are one of the first things to consider for your bike, my preference on the commuter bike is Tioga City Slickers.

I suggest you try the car / bike combo commute to start: On Monday drive the car to work and carry your bike along with everything you might need for the work week. Leave the car at work Monday night and ride your bike home. Ride back in Tuesday A.M. and drive home Tuesday night leaving the bike at work; Wednesday drive the car back to work and see how you feel about riding home that afternoon. Continue this rotation, increasing the bike miles and decreasing the car miles as you gain fitness and commuting savvy. This will give you the opportunity to see how the commute is, minimize the daily preparation you need to do and give you some flexibility and recovery options in event of an unforeseen event.

One more word of caution, once you start bike commuting you're going to have a tough time returning to cage jockey status

Hope this helps.