1. Last week I rented a Kia Elantra for ~$140+ petrol. I had the car Saturday to Saturday, picked up and returned to Denver International Airport, from Budget. Petrol is going for around $3.00/gallon right now, but rumored to be going up due to the BS in Libya.
2. yes, but they will usually charge you more if you do that type of arrangement.
3. Loaded question. Lodging prices will vary by location. A hotel in a popular destination (New York city for example) will be expensive, $250-$400/night. You can also get lodging for as little as $30/night, depends supply and demand. Food depends on the types of places you eat. You can eat at McDonalds for <$10/meal. You can eat at a 5* restaurant and pay over $100/person. I'd recommend looking @ www.hollyeats.com and chowhound.com for recommendations. Avoid chain restaurants (Applebees, Chili's, Ruby Tuesday etc..)
4. Tough call. There is a lot of nothing between the two coasts. Kansas, Nebraska, Iowa, Texas, Indiana etc.....are mostly farm land with little tourist interest. But then that is the heart and soul of America. I'd suggest starting in Boston, do a short loop into Maine (2-3 days), then go south. The places I'd recommend worth seeing are - coastal Maine, Cape Ann/Salem/Boston/Cape Cod(Chatham > Provincetown), Newport Rhode Island, New York City, Amish country west of Philadelphia, Baltimore Harbor, Washington DC, Williamsburg Virginia, the Outer Banks of North Carolina (you can drive one end to the other in about 1/2 day depending on traffic). Now you need to decide if you want to go west towards Atlanta or keep going south. Atlanta is nothing special, in my opinion. Coastal Georgia would be more interesting. When you get to Florida you need to decide if you want to spend a week seeing Florida. Florida takes much longer to drive than you might think, but then there are also lots of interesting places. The one place in Florida I highly recommend is Key West, which couldn't be further from the GA/FL state line.
Whenever you head west - New Orleans, Austin and San Antonio, followed by mega long stretches of desert to San Diego (best spot in S. Cal), drive through Hollywood to say you've been there(LA blows in my opinion), Santa Barbara, then take the Pacific Coast Highway to San Francisco.
If you can, Las Vegas, Lake Tahoe, Yosemite NP, Grand Canyon, Salt Flats in Utah and Yellowstone NP would be highly recommended too.
5. If you went Maine to Florida to California your talking about roughly 4500 miles. Assume your car gets 30 MPG, you will need 150 gallons of petrol @ $3.50 (high side estimate) = $525. Car I'd plan on $150/week = $900. I'd budget $100/night for a motel = $4200, you won't always need that much, but then sometimes you will need a lot more. For food, depends on your tastes. Unlike Europe, few US hotels/motels provide breakfast (some do, most don't), so I'd budget $10/breakfast, $10/lunch, $25/dinner or $45/person per day * 42 days = $3780. Then you need spending money. Some highways (primarily in the east) are toll roads, you will want trinkets, you will need to pay admission to some parks/museums, you will need buffer funding etc.. I reckon at least $500/week spending $. So another $3K. By my figures you will need $12,450 to do this trip.
If you drove 400 miles a day you could do this trip in less than 2 weeks, so 6 weeks will give you lots of time to see the sights.