Its very unusual to loose all communications with a country for almost 12 hours in 2017.
During Hurricane Maria, essentially all communications were cut with the Commonwealth of Dominica at about September 19, 2017 at 4:00am local time. It took nearly 12 hours to re-establish any communications with officials on the island via radio. There has been some unofficial communications with ham radio operators, assumed to be on the island.
All power, wireline, internet and cell service appears to still be out. Its unclear how much is due to general damage which will take a while to repair or specific points which could be repaired quickly.
There are some VSAT links in Dominica, but I didn't get responses from the ones I tried.
Initial aerial fly-overs by CDEMA/RSS, a joint disaster agency by 6 participating countries in the Eastern Caribbean, saw 70%-80% damage to buildings, the hospital and other infrastructure. The Barbados Coast Guard is sailing tonight towards Dominica trying to re-establish better communications for relief efforts. Additional relief personnel are due to be sent in the morning, during daylight hours.
At Sept. 21, 2017 01:00 UTC, partial telecommunications service was restored to Dominica. However, essentially 100% of the island does not have electric service, cell service is still out, and most people do not have service.
CDEMA/RSS has delivered 5 satellite telephones to the Dominica government and island emergency services. About 50 relief workers arrived from Barbados and now working to re-open the port and airport for further relief supplies and personnel.
Some people asked about satellite phones on Dominica earlier. Satellite phones are very useful after a disaster, but have some limitations during a catagory 5 hurricane. Satellite phones only work outside, not where you want to be during a hurricane. Satellite signals also experience rain fade in heavy storms, so you need to wait until the hurricane clears from the area. Satellite phones also need batteries or power, which tend to fail just when you need them. I don't know the exact details yet about what happened to the telecommunications on Dominica.
Some ham radio operators have been verified as operating from Dominica. Its an unfortunate, but necessary thing that needs to be verified during disaster communications.
I'm not clear what you're getting at here. Are you saying people are faking operating from the islands? That seems unlikely. Basic RDF is going to tell you in short order where they are transmitting from. And for the smaller islands, the local operators are well known in the region, so it seems unlikely someone would be able to set up shop in, say, Tennessee and claim to be a new ham who just moved to Anguilla last week.