Brunei Passport, UK Residence + Permit, trying to go on a cruise in the Caribbean - double check my conclusion?

I have a Brunei passport (I am a Brunei citizen) living and working in England, UK (I have ILR and a Biometric residence permit).

My travel itinerary and Visa research returns the following. Can anyone help me double check or point me at resources?

1) USA - ESTA [ http://www.esta.us/brunei.html ]

I've done this before in the past, I hope it shouldn't be a problem.

edit - official site [ https://esta.cbp.dhs.gov ] provided by commenter

2) Half Moon Cay (Bahamas) - No Visa required

[ http://www.bahamas.gov.bs/wps/wcm/connect/bf838397-2677-410e-9987-87fa188e4966/Visa+Requirements+for+Visitors+Travelling+to+The+Bahamas1.pdf?MOD=AJPERES ]

3) St. Thomas Island (US Virgin Islands) - Same as USA

[ http://www.frommers.com/destinations/virgin-islands/planning-a-trip/entry-requirements--customs ]

Question - if I have a Visa Waiver from visiting the US, would it apply here?

4) San Juan (Puerto Rico)

• same as USA [https://www.worldtravelguide.net/guides/caribbean/puerto-rico/passport-visa/ ]

5) Grand Turk (Turks and Caicos) - This one I'm not sure.

i) http://turksandcaicostourism.com/immigration-turks-and-caicos-entry-requirements/

ii) https://www.visittci.com/travel-info/passports-and-visas The link in ii) suggests that I don't need an additional visa, as I already have ILR for the UK Seems like I need to apply for a rather expensive Visa even just for a quick visit?