I would think that most publicly available heliports will be run as a separate entity from the chartered flight businesses that land there. In the case of Battersea, up until the recent change of ownership, the group that ultimately owned the heliport (Von Essen), also owned a charter company (Premier) that used the Heliport, but they were separate legal entities.
As to their accounting representation (fixed assets etc.) I'm sure there are people better able than I to help you but I'm not sure that's the main thrust of your question.
Can't help you with a world survey of profitable heliports, but you'd have to assume that the ones that have been going for a while such as Battersea in London, and the Manhattan ones must have something going for them. On the other hand there have been attempts to set up other ones (eg. Breeze at Dagenham to the East of London) that never really got off the ground.
On Frequencies, Battersea in London, and Issy in Paris have just one each. On fees the best thing to do is to research them directly, but to get you started (and I suspect to set the range !) Battersea's is
here, and Issy in Paris is
here.
HTH
PS Aha. I get what you mean by frequencies, ie. movements. Tricky question that one. You really need an outline business plan to answer that one. For example Battersea is restricted by legislation to 12,000 (from memory) movements a year, and is the only generally available public heliport in Central London. As a result it can charge pretty much whatever it likes to generate the required return. The Paris one is run in a very French way as a service, so charges are much smaller, but I suspect do not cover the costs of operation, and certainly not the cost of capital employed if you include the land.The only way you can answer that question for your situation is to build some models based on the costs you think you'd incur and your required return on capital.