With the current market and foreseeable future, no, engineering degree won't open doors in finance unless you're 1st class and get in through MA programmes. 2nd upper, maybe, if you have incredibly strong CCA records. Remember who you're competing with - the business and finance grads - so you need to have much more solid credentials if you want a fighting chance.

For now, almost every bank has frozen their headcount. Even business students from SMU can have trouble finding work there. If things change 4 years later and you graduate in a bull run, then things might be better.

Chem eng will probably be a lot more competitive than you think. Don't under-estimate the bell curve. A lvl is nothing, in nus chem eng, everyone is straight As. Your life might be easier in ntu. Yes, ntu is easier. If i were you, i'll switch to a less competitive course. Be a big fish in a small pond.