Debit card requirement is usually very basic.
Minimum age of 17 or 18. Not too sure about that. The most basic
of debit cards are issued by DBS/POSB.
Gotta check on that yourself. Yes, you can go to any bank to
enquire. But due to the infamous long queues, try calling them up
instead.
MasterCard or Visa doesn't really matter much. At such a young
age you won't be using much of the offers or promotions that might
come with it. Probably just use it to draw money overseas.
Also, please note that some debit cards have a minimum
expenditure per month to ensure that the card's annual fee is
waived. But even if you do not manage to spend the minimum amount
needed to have the annual fee waived, the sum is still very
low.