No, they're more expensive because they have higher infrastructure costs. Building and maintaining hundreds of kilometers of track costs a lot.

Prices are set by what the market supports due to the value the product provides, not what the product costs to deliver.

Yes and no. The market has to at a minimum cover the cost of operation otherwise businesses will stop operating.

Not true, many industries don't return profit and are yet subsidised by the government out of necessity anyway, eg: farming.