Sorry can't help much about your airline/visa questions. All I know is GA (Garuda) has much better schedule MES-CGK-DPS.
Time from airport to Grand Hyatt (in CBD) is about 45-60 minutes at around 11-11:30am.
Return may take much longer though if you depart around 6-7pm (due to rush hour traffic).
Departure tax of Rp. 100,000 is for international flights only. The domestic tax is much lower, IIRC Rp. 20,000.