Thanks for your questions and specifying which project opportunity you are working on. There are several resources on the ‘Design Area 2: ICT’ page that will help answer these questions.
For example, the Telecommunications chapter in the National Indigenous Infrastructure Guide provides a typical estimate of remote communities which can be extrapolated to the Cape York region (see page 281 for speeds).
The Mobile Coverage Report will also help you determine the approximate percentage coverage of mobile connectivity across Cape York.
As stated in our overview of network coverage across Australia resource, you can also view the number and spacing of mobile towers in the region here: https://www.rfnsa.com.au/
Generally, internet coverage (such as via NBN) is increasingly common on the Cape, however there are still significant amounts of offline areas once people move away from their wifi if they have it, and away from major communities. A satellite phone is required to ensure they have some coverage in these ‘dead’ areas but not everyone has one.
I hope that helps, best of luck with your project,