Our team has the same dilemma. Tools and small parts aren’t too difficult; pack them in a sturdy, airline-safe box and check them as baggage. Some items could go in team members’ luggage. Valuables should go as carry-on. Be sure to study the TSA guidelines. Sharp tools should be checked, but batteries must be carry-on. If you watch the weight, cost should not be a big deal. The box of tools could be someone’s “second bag.”
The most difficult part is the batteries. They are NOT allowed in checked baggage, but may be allowed in carry-on baggage. One year, each student on our team was handed a pair of batteries in a box, and they merrily went through airline check-in, TSA security, and onto the plane lugging batteries! Except one of our mentors, the last one to check in, was stopped. On the return flight, our students were lugging huge trophies instead of batteries. 
You could call the airline and ask, but if the TSA nixes the idea, you’ll be at the airport with no way to bring your batteries.
It seems to me the safest idea would be to ship the batteries directly to your hotel via UPS Ground or something. Make sure you have trustworthy arrangements for shipping the batteries back home. Most of the downtown hotels have a concierge who can assist with this task. So call your hotel to verify what arrangements can be made.
Regarding other questions:
According to the Google map, the straight distance from the pits to the Georgia Dome is about 1000 ft., which is nowhere near a half mile, more like a quarter mile. The problem can be bottlenecks at the escalators, when crowds of people are all trying to go one way at the same time. The big distances are walking to the venue from downtown hotels–you have to cross the entire Centennial Park and pass Halls A & B of the GWCC, which are equivalent to several blocks. If you stay at the Wyndham Garden Inn, for example, it’s about 14 blocks to the pits.
If you’re thinking about saving money by renting cars and making picnic lunches, especially if you’re staying downtown, be aware that you will have to pay for parking at the hotel AND at the venue. And the downtown area has no supermarkets to speak of. If you want to buy food at a supermarket, perhaps your team could rent just one vehicle for running errands, and everyone else can walk.
Don’t expect the downtown hotels to have either free breakfast or free Internet. Usually they charge per day per computer. Sometimes you can sign up for their “membership” program and get free Internet.
Don’t expect a free hotel shuttle from a downtown hotel to the airport, either. Only the airport hotels have a free airport shuttle. Our team stayed near the airport one year. The shuttle took us to the airport (1/2 hour), then we took MARTA to the Georgia Dome (another 1/2 hour). This is why our team now prefers to stay downtown. Airport taxis in Atlanta charge per person. Atlanta ain’t cheap.
As others have mentioned, you can eat in the Peachtree Plaza (which is only open during normal mall hours, so no early breakfast) or in the CNN Center food court. Some places in the CNN Center are open for breakfast, and the food is comparatively cheap. I don’t know if breakfast will be available in the GWCC food court this year. The Georgia Dome itself has a greater variety of food than most of the Regional venues I’ve been to.
One other thing for us Westerners. Spring weather in Atlanta is variable. If it’s warm and sunny, lunch can be a picnic on the grass with Frisbees and shorts. These are the fun times people like to remember. But things can get really wild–pouring rain, gusty winds, lightning, freezing, hurricane, tornado–and you can get soaked in an instant. So usually teams have no problem walking from the hotels to the GWCC, but it’s good to bring along weatherproof outerwear.
