Just as a point to clarify, would you have say 75 minutes layover time at Changi? If so, that should be enough time to go groundside, mail the packages from the Post Office at Terminal 2 departures and get back to airside. Unfortunately I don't know the answer to your questions but if you are asking about the mobile post offices then I assume that you are arriving at either T1 or T3. If no other poster can reply you here, your best bet is to get to the Mobile Post office and ask your questions. If they can't take your package, assume that it would take 10 minutes from that point to get groundside, then another 10-15 minutes to get to the T2 ground side post office (skytrain), then 15 minutes to get to your departure gate after leaving the post office.

You can also try this site, see if Sing Post will answer your question:
http://www.singpost.com/feedback/feedback_sp1.asp