Honestly, I don't know if what I did actually solved the issue of if it was problem with the Telco (Celcom) or Apple's side that got rectified in that time. Anyway, here's what I did;

Tried everything listed on this thread, but no change. I then went to Settings > Messages and removed (untick) all the mail addresses associated to iMessage and then disabled the "Enable iMessage" option on top. Did the same for the FaceTime settings after that. Then rebooted the phone. Then went back into Settings and enabled both of them again. Just let it wait for a couple of hours (the spinning thing next to the greyed out phone number) and after a couple of hours both iMessage and Facetime came back and there was a tick again next to my phone number. Touchwood it doesn't happen again.

Shouldn't be a problem with SG set. I've used SG and AU sets in the past with Bolehland telcos like Digi and Celcom. Just make sure your time zone (Automatic: Kuala Lumpur) is set correctly in the Date & Time settings. Not sure if I can help you, since I don't use Webe. Sorry ... I checked this forum and it seems there are some other Webe users (click: example) experiencing activation failure with iMessage. According to Apple's troubleshooting page you might need to wait 24hrs after performing the steps. If it doesn't resolve itself, you might need to contact Webe. It also might be a good idea to check Webe's official Twitter or Facebook to see if anyone else has reported iMessage/Facetime issues.

Unfortunately webe does not support iMessage and FaceTime.