Somehow I ended up learning that gmail log-in and google log-in to RuneScape aren't integrated and bought Premium Membership 1 year for non-existing acount (how is this even possible). I've searched through support thread and sent a ticket on 31st December. It's 2nd January and still no reply. I have all payment confirmations etc. I'm worried I might have to pay again, or will Jagex transfer that membership?
You won't lose the days as membership will re-start from the transfer date.
However the delay on responses is significant. During December, players were waiting 2-3 weeks for their tickets to be dealt with. I am not sure what the current delay is but it might still be 2-3 weeks.