well, its quite similar to most of the words u listed up there, if you look them up in the dictionary u might be confused.
fee: money you pay for goods or services. you exchange money for something.
expense: kinda like "fee", but sometimes u dont get tangible returns.
charge: in most cases, same as "fee"
fare: usually "fare" is a cost involved transportation, like taxi,bus/ferry tickets, personally i prefer to use this word on public transit only.
rate: has something to do with level, or range if you would, "rate" can also be used to indicate exact pricing or a range of prices.
the hotel room charge will also include your pickup from the airport.