It may be different in more economically active parts of the country where there seems to be a trend where villages within easy driving distance from major towns effectively become rural suburbs where people move to but still live like they are still in the town. For example, they drive to work in the town and shop in the town and use the town's leisure facilities. They just live in the village without using the village shops or services or interacting with 'locals'.
Yes, that's true. There are already many places like that in South Wales! In order to try and negate such an effect, such dormitory towns and villages could not be classed as rural. I would base such a classification around population, density of population, and distance from large centres of population.
The easiest way would be to increase fuel taxes to ridiculous ammounts. This punishes inefficient drivers and vehicles, and acts as a very effective road-pricing scheme in that, the more you drive, the more you pay.
Yes, that would certainly encourage less car use, though I doubt anyone would ever try and do such a thing due to the inevitable protests.
What we do need to do is address the issue that exists, if only in people's minds, that the fixed costs of owning a car make it sensible to use it as much as possible rather than leaving it parked up.
This means, as you say, increasing the costs paid at point of use, whether this be by fuel duty, road pricing, tax, or a mixture of methods.
At the same time, we need to look at ways of making public transport more attracive and accessible as an option, through more frequent services, easier ways to pay, longer operating days, more integration and a more comfortable travelling environment.