US refugee travel document from JFK to Sri Lanka

AS SOON AS POSSIBLE! I am writing this now and after 8 hours I have flown via Dubai to Sri Lanka. My situation is: I recently got asylum, got FTE and now drive from New York via Dubai to Sri Lanka. My question is
1) Do I need a visa?
2) Is there any customs / border issues in Dubai? Sri Lanka?
3) Should I only use RTD for the entire journey? (I still have a valid citizen from my home country) or do I have to use my passport?
Please help me?