Don't take my word for it but that is pretty much unheard of these days. Focus on your diploma and apply to university. Banking is ultra-competitive and even if you have a 1st class degree from a top university you are not guaranteed a job. I am currently applying to banks and I don't know why I'm bothering, it is like banging your head against a brick wall.
This is the best advice I can give you. Open a micro trading account and learn to trade, and practice every day. While you're studying you'll have loads of time to trade the London session. That would coincide with your evenings in Singapore. There is loads of information on the net - no need for textbooks, seminars or out of the box 'systems'. Learn the basics of money management, support & resistance, trend lines, and you will make money one day. Once you can earn a bit of cash from summer jobs and the like, maybe in your later teens & twenties, you might be in a position to open a larger account, and you'll have plenty of screen time behind you. Patience and discipline and you will eventually get there. I say this as someone who is 25 and just got to the stage where I'm trading profitably, after dabbling with plenty of failures in my early twenties at university. Time is on your side.
Not to sure about the world of proprietary trading firms to be honest, do some Googling. The idea is you trade for them with their money and you get a cut of your profits. FXCM and the like are brokers and make their cash from spreads charged to retail traders.