Captain reported an unclear departure clearance and language barriers contributed to the need to deviate off course after receiving a terrain alert on rising terrain ahead.

Narrative

Near CFIT. A flight departed ZZZZ. The flight was operated with Aircraft X under an IFR flight plan. The crew had been awake the previous day since XA:00 AM; had been called to duty at XI:00 PM and assembled at the hotel lobby to ride an airport shuttle. But at XI:20 while still in the lobby the crew received a phone call and told to standdown; the flight was rescheduled for a XQ:00 [night time] arrival at ZZZZ; leaving about 0:35 minutes before from ZZZ.The Captain's headset was new but not working correctly; providing only transmit and no receive service. The problem was detected three days before and cause undetermined. Crew navigation was provided on Aircraft X with a Garmin GTN system with terrain warning feature. Also; the crews were issued company iPads and Foreflight software; which linked to the Garmin GTN. However; the Captain's iPad did not have ZZZZ airport charts for arrival/departure; but only displayed the airport runway. This was later discovered to be a limitation of the purchased software licensing by the company. Additional staff had been hired; taking the remaining licenses. The First Officer's iPad did have charts for the ZZZZ airport for approach; and was used for the arrival.An IFR clearance was received by the First Officer and conveyed to the pilot. The clearance was to depart Runway XY; fly runway heading to 10;000; then turn right on course; maintain flight level 270; '. The Captain questioned the clearance due to not having radio receiving headset. The First Officer repeated the clearance; but then changed it say; 'fly runway heading; report leaving 10;000 feet'. Then the First Officer stated they were not sure; and restated the original clearance as 'fly runway heading to 10;000; then turn right on course'. The flight flew runway heading for about eight miles south of the runway. Visibility was over 10 mile and nighttime conditions. The first officer noticed the Garmin GTN displaying a yellow Terrain Alert. Looking outside; the crew saw rapidly rising terrain with tops about 10;500. An immediate turn to the west to safe space was initialed by the Captain; using the autopilot. A climbing turn to the north continued and on course. A near CFIT event was avoided.IFR Clearance to fly runway headed until 10;000 feet; then turn on course. This was unclear to the Captain and was received from the First Officer through [foreign] air traffic control. No iPad database for ZZZZ airport. No Runway XY departure procedure information. Headset not working correctly. No receive feature for Captain. Language differences; English/Other Language with ATC language differences; English/Other Language with ATC. Long 18 hour period awake for tired crew.Solutions. Get correct IFR Clearance. Review airport and runway departure procedures. Update iPad database for airports. Have an operating headset. Resolve crew communication differences before acting. Maintain visual observations during climb out; note terrain and obstacle avoidance.