Welcome to The AnswerBank!
I'll tackle the 'being away from parents bit first': I used to teach Year 13 students (which is the UK's equivalent of your 12th Grade, since formal education starts a year earlier in the UK than it does in the US). When they were applying for university places, the advice I always gave them was that they should only to apply to universities that were far enough away from their parents to ensure that they couldn't possibly get home for the weekend. There were two reasons for that, viz:
(a) however mature (in comparison to their peers) a young person might be at that age, they will still benefit from 'being away from Mummy's apron strings' while at university ; and
(b) university should be about much more than simply studying. The social life at university is just as important (if not more so) than formal study if one is to get the best out of the university experience. Students frequently miss out on that side of things if they're constantly heading home to their parents.
With regard to UK visa rules, see here for general information about applying for a student visa:
https://www.gov.uk/student-visa
The University of Cambridge website provides further information about the restrictions on working with a student visa:
https://www.internationalstudents.cam.ac.uk/student-visa-responsibilities/working-student-visa
If you can find a place at a UK university, and the financial situation is acceptable to you, I'd strongly recommend coming to the UK. The very fact that you've asked such a well thought out and well-considered question suggests to me that you've got the maturity to thrive in a UK university setting.
Applications for universities in the UK are handled in the first instance by UCAS (the University and Colleges Admissions Service). Their website has loads of information for international students
https://www.ucas.com/undergraduate/applying-university/ucas-undergraduate-international-eu-students
The UCAS search facility, enabling you to find suitable course providers, can be found here:
https://digital.ucas.com/search
If you need advice as to whether a particular town or city in the UK would be a good place to study (with regard to factors such as accommodation provision or whether there would be a good social life on offer), feel free to ask further questions on this site.
We might also be able to advise you about the best universities for your particular area of study. While Oxford and Cambridge are traditionally regarded as England's 'top' universities (akin to Harvard and Yale, and just as hard to get into), other universities might be better for specific subjects. e.g. if you want to study Marine Biology, Southampton University might be a good choice. For Environmental Science, the University of East Anglia is a first-rate provider. For engineering, UMIST (the University of Manchester Institute of Science and Technology) would be an excellent choice. . . . and so on.
Go for it!