1. No, in this instance, there is a difference between "a charge" and "a rate". A rate would not make sense in this sentence. A charge (in this context) is a specific amount of money that this company would want from you because you didn't cancel your booking in enough time. You would need to pay that amount of money (the charge) to this company. If you don't pay that charge to the company, they may charge you more money, and you'd get yourself deeper into debt with this company.
2. Yes, the term "charge" and "admission fee" could be used interchangeably here. The term "charge" in this sentence is referring to an "admission fee", so you could use either term and it would make sense.
3. Yes, based on what this sentence is saying, the "one off charge" seems to be referring to the fact that you would need to pay a specific amount of money to this person/company/etc. to obtain a good/service of some sort.
I hope that makes some sort of sense!! :D