Hello, thank you for your question.
Myself, I have completed 4 A Levels; although in Biology, Chemistry, Psychology and Sociology. Doing 4 subjects is challenging; but it is definitely achievable if you strongly prioritise academics over your other commitments such as part-time work/hobbies/social life, etc; you are strongly interested in all of the subjects; have the necessary background knowledge in all the areas; and have the access to the appropriate support. However, you are certainly going to have to put a lot more work in than the majority of your peers to obtain the results you want. Hence, generally it is only advisable to take 4 A Levels, if you think this would benefit you academically and/or professionally. It sounds like this might be true in your case; but of course, at the end of the day, only you have the full understanding of your situation and are in the position to make this decision. Although, obviously talking about this with academic/career advisors, your teachers, parents, friends, etc., as well as, doing a comprehensive research into the type/amount of content that you will be covering, could help you to come to an objective conclusion, concerning whether or not you can realistically manage the work-load and enjoy your college experience, too.
In terms of the subject choice, I can see why this decision is so difficult to make. Considering that you are interested in both Medicine and Engineering, you will definitely need Chemistry and Maths A Levels to meet the entry criteria, set by the vast majority of universities. However, content-wise for Medicine, honestly-speaking, Biology is also a-must-have; even more so than Chemistry, since majority of the module content will be biology-based. Also, as you have mentioned Physics may be needed for the Engineering degree of your choice. Deciding between Medicine and Engineering as a career route would certainly clarify which subjects are better to take; although, understandably, you may not want/be ready to make this decision right now. Regardless, if possible time-wise, I would definitely recommend trying to undertake some work experience in these fields, since this could give you some further insight into which path would be right for you. Similarly, looking at precisely what is job involves, including factors such as the pay, work environment, job stability, etc., could help you to pin-point where your interest truly lie; and which job would better suit you preferred life style, personal needs, and so on...
Concerning whether it is worth doing an EPQ instead of an A Level, I would say that while advantageous, an EPQ does not hold the same weight on an UCAS application as an A Level or even an AS. Certainly, an EPQ is great to talk about on your personal statement (since it gives you research & writing experience, etc); however, in terms of meeting the actual entry criteria, the majority of universities will not accept EPQ as one of the qualifications. Hence based on my understanding of how much work an EPQ requires/its benefits, I would only advice undertaking this extra project if you are considering to apply for highly competitive universities and/or have the time for and personal interest in researching a specific topic area in great depth and in a university-style manner. Furthermore, there are many other things beside obtaining an EPQ qualification that you can do to make your personal statement highly attractive to universities such as engaging in further subject readings; gaining some work experience; taking part in other college projects/competitions, etc. Thus, overall, it may be possible to indicate a similar level of an experience that an EPQ provides you with in other ways; and hence, deciding whether or not an EPQ will be of real value to you will depend on what other extracurricular activities you have/or are planning to take part in, and how similar they are to the EPQ itself.
I hope this helps. Let me know if you have any further questions
Best Wishes,
Kasia (4th Year Medical Neuroscience Student, MSci with a Year Abroad)