You can try to book your ticket on CX.com and check if your ticket class allows stopovers. This is a bit tricky... you'll need to enter your passenger info and proceed to the payment page and on the bottom there is a link that will take you to the fare rules. Under that, you can check if stopovers are allowed.

For example:

Stopovers:

1 - PSGR P1 ADT RULES DISPLAY
FARE COMPONENT 1 ADT XMNJKT CX SLOWIBS4 PU 1 S
FCL: SLOWIBS4 TRF: 884 RULE: C169 BK: S
PTC: ADT-ADULT FTC: XOX-ONE WAY SPECIAL EXCURSION
SO.STOPOVERS

2 FREE STOPOVERS PERMITTED ON THE PRICING UNIT IN HKG


I don't think there is a limit on how long you can stopover, as long as it's within your ticket's maximum stay.

You will definately need to pay the HKG airport tax.