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Any trip is achievable if you want to do it badly enought. I'd think for a trip like this you'd need about 3 weeks just to cover the distance at a pretty good pace. From there, add on whatever time you think you'll want for sightseeing, exploring, rest from the road, etc.

Its hard to start putting numbers on expenses, without knowing more about how long you'll be on the road, where you'll be staying, what you're driving, etc.

Renting a car with multiple drivers won't be a problem, but you should expect to pay a fee for each additional driver. Anyone who is going to drive the car needs to be on the rental agreement, so you really can't skip this to try and save money - it could result in serious legal problems if you had a problem while on the road.