Easy question first: if the rim is not too warped it can be "trued" back to roundness by using a spoke wrench to tighten/loosen the spokes. This is pretty easy to do as long as you're careful and make small adjustments - there are several video tutorials online that will all explain the process in detail. You could pay a shop to do this for you, but basic wheel truing is a good skill to have for commuters.

And the more difficult issue: an eleven mile commute when you're not in shape or experienced with commuting is going to be tough to start. Certainly doable, but for the first couple weeks you'll really have to persevere. Odds are you would be able to commute more quickly using a road bike, but your old hybrid will suffice as long as it's mechanically reliable.

One thing you might consider trying at first is an on-off schedule: drive your car to work in the morning of the first day and bring the bike along, leave the car there and ride home that evening, ride to work the morning of the second day, and drive home the second evening. This would give you a chance to try out routes and establish how long it will take you to ride, without risking total burnout.