A language barrier contributed to a track and clearance violation for a corporate jet flight crew on an arrival to TAPA.

Narrative

Approaching TAPA with scattered thunderstorms in area. ATC instructed to descend to FL 140 and asked if we could accept visual approach. I affirmed that we could once below clouds. We were then told to descend to FL80 and to proceed to OMREY intersection (approximately 10 miles on the centerline for Runway 7). We proceeded as instructed and upon turning inbound in visual conditions with runway in sight; Crew advised were too high and needed vectors or a turn to descend. ATC cleared us to hold at 'the fix'. Prior to reaching missed approach fix; ATC gave us a heading. We complied; were re-turned inbound and landed on Runway 7. Upon landing; FBO said that the Tower wanted to speak with us. After deplaning owners; I called Tower as requested. Spoke with supervisor who asked me how we were cleared. I did as contained herein. Apparently; ATC expected us to hold in a descending turn over OMREY rather than flying to the missed approach fix. Significant contributing factors were lack of standard CIAO phraseology; seemingly odd requests (visual approach then expected to hold over a fix without instruction) as well as very poor English. I have flown throughout the Caribbean; Mexico; Central and parts of Europe yet have never experienced such poor English from ATC. Anywhere. Looking back; I see that we could have refused the visual approach as well as confirmed each instruction more thoroughly.