How do I switch to self-study at home instead of Sixth Form (I'm 16)? Do I have to have my parents' permission? Am I required to enroll with an online school?
You need to find somewhere to sit the exams first, so that you know which exam boards they offer. It costs quite a lot to enter privately - as well as the exam board fee there will be admin fees charged by the exam centre.
Some subjects are very difficult to take at home - eg sciences because of the practical requirements, anything with coursework.
You don't need to pay for any sort of tutoring - you can just study from textbooks etc, but it is worth having some sort of input at some point, especially for exam technique.
You really need to have your parents agreement - it will cost money to sit the exams, and to pay for whatever tuition you decide you need, plus textbooks etc. Plus, if your parents get Family Allowance they will lose it (they can only claim it if you were homeeducated before the age of 16)
Lots of information here -http://he-exams.wikia.com/wiki/HE_Exams_Wiki