What should I study to get a career in EEE(robotics)/quantitive finance

Background
I am in Sixth form (Y12) in the UK. I study Mathematics, Further Mathematics, Physics and Computer Science

I recently learnt about this quant field and it interested me because I have always like math's, I started programming a few years ago really enjoy it and I recently started learning to trade which has exposed me to the financial markets and basic economics which I find interesting. So now I'm thinking a job in the quant sector would be amazing.

I am also interested in electronic engineering in like robotics, devices and human and machine integration (a bit of a pipe dream)

It is around the time now in the UK where we are being told to think about University and our careers so I would like some advice on what I should study.

I have found different courses which I would be happy to study but none of them really have all of my interests because I would like to keep my options open.

These are links to some of the courses: electronic and electrical engineering, computing with finance and management, electronic and information engineering.

Questions
1. Is it best to study a degree with 1 job sector or career in mind or is me trying to keep my options open a good idea?

2. How can I find a course that applies to all my interests?

3. Can I get into the quant sector by doing engineering degrees like I have linked above and then doing a financial engineering masters?

4. What are the best courses I can study to get into the quant sector?

5. What are the best courses for robotics?

6. How do I know if I am truly interested in something.
(👇Rambling 👇)
I feel I am interested in all theses jobs/industries/topics (whatever you see it as) but then I sometimes feel like I just like them because they are cool or something. I don't know. Its like when I was picking my a levels people were like do you REALLY LIKE these subjects and I think yeh I do(but its not like I'm gonna kill myself doing them. I just enjoy them. I mean everything gets boring at a point.)

Thank you very for much! : )

p.s. for reading a near essay

I can answer a few of those questions.

1. Is it best to study a degree with 1 job sector or career in mind or is me trying to keep my options open a good idea?
Probably to keep your options open. It's my motto, but at the same time it depends on what the entry requirements are for those specific industries/careers.
As far as I know, you can go into quants with an engineering degree, but you will struggle to get into an engineering grad scheme with a degree in finance (or financial mathematics). So I would play it safe and go with a degree in electronic engineering.
A degree in robotics isn't necessary going to limit your options that much, but it seems like a very niched field i.e. you don't normally get a lot of employers or professional qualifications asking for degrees in robotics. It's more likely you will get people asking for degrees in electronic engineering.

2. How can I find a course that applies to all my interests?
You can't as far as I know. If you're looking for something that involves robotics, electronics, and mechanical engineering, you might be able to find something in the engineering field. On the other hand, it's incredibly unlikely that you will find something that would marry both engineering and finance in one degree. It's likely that you will need to do at least 2 degrees/qualifications in order to meet this requirement.
I don't know how you intend to become competent in quants, but you can consider the following:
The routes into robotics are generally:

My plan of action would be to do an undergrad in electronic engineering (or something along those lines) and then do a CQF. If you prefer getting a master's degree (I can't quite understand why, but whatever floats your board), they would normally ask for people with a quantiative background e.g. an engineering degree

3. Can I get into the quant sector by doing engineering degrees like I have linked above and then doing a financial engineering masters?
Yes. I think most of the employers care about whether you have the numeracy and programming skills. These imply that you have done a degree in some mathematical discipline e.g. engineering, physics, maths, financial mathematics (maybe).
In terms of doing a financial engineering degree, you will need to check the entry requirements of the specific degree. For example you should be fine with the following:
You are unlikely to be OK with the following:

4. What are the best courses I can study to get into the quant sector?
Hands down, CQF. There are master's degrees available, but I consider the material a bit too theoretical. CQF on the other hand uses more practical application.

Possible key words that you might want to look for can include:

A lot of the degrees for the above would be at master's level. Financial mathematics do have some degrees at bachelor's level though.

Do note, you can go and do a postgrad degree in something related to finance with an undergrad in engineering, but you can't go an do a postgrad in engineering with an undergrad in finance.

See the following for how to become a quant:
https://uk.indeed.com/career-advice/finding-a-job/how-to-become-quantitative-analyst

You would probably want a second opinion from someone who works as a quant regarding the above.

The BEST subjects are Physics with Maths/Computer Science (target Edinburgh, Imperial, UCL, Cambridge, Oxford, and Manchester), and Mathematical Economics (LSE, Imperial, UCL, and Cambridge), PPE (Oxford, Durham, UCL, and LSE), or Chemistry (Oxford, Cambridge, Imperial, UCL, Edinburgh, St Andrews, and Bristol. Also, look at open learn courses (MOOCs) at LBS and ICMA Centre in Finance.

When you start your degree aggressively go after every opportunity to gain experience in the sector - holidays, mid-week during term, etc. You also need to do a team sport and represent your uni, as lots of people apply from top-tier uni. You have to show that you are competitive and tenacious - and not dull, as you will have to network with clients. If interested in comedy or drama do the Edinburgh Fringe. Bottom line - be interesting and engaging.

are these unis the only target unis? i was considering applying to uni of bristol mathematics

what degree do you think would be best suited for quant finance

mathematics, mathematics and computer science or mathematics and statistics?