I just recently wrote a very detailed review about the WiFi on the A350's including speed tests on two different flights.
SQ Y and PE to Iceland with Iceland Air (testing all the WiFi…)
The WiFi is not free for anyone even PPS card holders in Business Class... Everyone must pay or log in using a roaming partner (either iPass or Boingo).
Currently, a 3-hour pass costs US$16.95 and a 24-hour pass costs US$21.95.
If you're connecting to another SQ A350, B777 or a Scoot 787 flight then you can continue to use the 24-hour pass whilst onboard (but note the 24 hours is valid from when you first activate the pack and can't be paused).