driver licence - guess you could renew it but need to re-sit for the road test. don't think you can do it within 2 weeks.
for the health card, there is a grace period for 3 month. so even u apply right after you arrived, you will not be able to get your new health card within 2 weeks.
both need a valid mailing address to send the new card over to you....
I wonder if the bank statement must be "mailed" to you in order to become an address proof ........ because nowadays people (including me) prefer to receive e-statements rather than mailed statements!!
i went to the bank to ask them to print a statement for me with the bank stamp/date stamp to proof that's the true copy.
as you mentioned e-statement could be fake. or if you have insurance policy, ask your broker or agent to mail you a statement with the address is another alternative.