May I know how are translators paid here? Do they liase on their own (email, etc) with the project owner and determine their payment method there, or...
Yes, clients can post notices of potential jobs on ProZ.com, and translators can bid on these jobs via ProZ.com's system, but starting from the point that a client selects a translator, all correspondence is done directly (not via ProZ.com), e.g. via e-mail or Skype, and all delivery, invoicing and payment is arranged directly between the translator and the client.
...does ProZ provide its own secure platform to let payers pay translators?
No, for ordinary members, ProZ.com does not provide a payment platform.