Publius

Who was "Publius" (Acts 28:7)?
He was "the leading citizen of" (Acts 28:7) Malta.

Who are the "us" (Acts 28:7)?
Unless Publius was an exceptionally rich man who "entertained" (Acts 28:7) and "provided" (Acts 28:10) for all 276 passengers from the ship, it is likely to have been a smaller group that included or was limited to just Paul, about whose incident with the viper Publius may have heard about, and Paul's companions Luke, Aristarchus, and perhaps the Roman centurion.

Who didn't heal Publius' father "of a fever and dysentery" (Acts 28:8)?
Luke, who was a doctor.

Why did God have Paul heal Publius' father?
So that "the rest of those on the island who had diseases also came to be healed" (Acts 28:9).

What must they, their families and friends have heard from Paul during the "three months" (Acts 28:11) that he spent in Malta?
 

What happened after those three months?
Spring arrived and the wind changed so that they could sail north to Italy.

What is meant by "an Alexandrian ship whose figurehead was the Twin Brothers" (Acts 28:11)?
A ship from the port city of Alexandria in northern Egypt whose figurehead was two figures who apparently were brothers in the pagan Greek mythology. North Africa was the breadbasket of the Roman Empire at the time, so this may have been a grain ship bound for Italy.

Where is "Syracuse" (Acts 28:12)?
Syracuse is a port city on the east coast of the island of Sicily and is about 90 miles (145 kilometers) northeast of Malta.