My question is what services should I expect to be billed for?
You should be billed for everything - every appointment, every treatment, every prescription, all non-emergency hospital treatment etc..
The only thing you should not be billed for is A&E emergency hospital treatment, which is free to all.
If they are only charging you for prescriptions, then you are being treated for free on the NHS, which, as you know, you are not allowed to do on a visitor visa.
So, you must insist that they bill you for every single thing - if you visit the doctor to get a prescription, you need to pay for the appointment and also pay the non-subsidised NHS fees for the prescription. If you need a consultation appointment, you must insist on being billed. If they try to tell you it's not necessary for you to pay, then you need to keep insisting until they give you a bill.
The NHS is required to treat everyone who needs treatment - whether they are entitled to free NHS care or not, they can't turn you away. They often don't realise that some people need to pay because it is the norm that everyone gets free treatment - they rarely come across people who aren't entitled to it, so they are usually unprepared to bill you for regular appointments... which is why you need to make sure that you pay for everything, even when they say you don't need to.