[Raak] NO, not involved in building.
[INJ] NO, not known for his beliefs.
[CdM] NO, no medical connection.

OK, we're looking for a British man, born in the 17th century, became famous and died in the 18th. He died violently, but not unlawfully (subsequent research suggests there might have been some doubt about the legality of the circumstances leading to his death, but that's probably misleading; he certainly wasn't murdered) although he was not executed, nor killed in a war or a duel, nor did he commit suicide or die in an accident. He is not mainly known for his death (although the manner of his dying is at least somewhat celebrated).
He spent a lot of time in boats, but was not a noted navigator or explorer. Nor was he a politician, scientist, writer, aristocrat or inventor, and he was not involved in the arts, construction, geography or medicine.
He is believed to have been involved in a war in some capacity closely connected with the way he became famous. He has nothing notable named after him.

[Raak] YES, I should say justifiable homicide.
[Tuj] YES, he was an infamous lawbreaker.

[Tuj] YES! Our mystery man was in fact the notorious pirate Edward Teach (or Thatch, or any of a variety of other creative 18th century spellings), aka Blackbeard.
He probably acted as a privateer during Queen Anne's War and subsequently turned pirate. Killed in battle in 1718; his Wikipedia article suggests that the governor of Virginia overstepped his authority by sending troops into North Carolina to attack the pirates, hence the doubtful legality.
One baton in the shape of a yard-arm with a severed head hanging from it goes to Tuj.

[jim] It was your answer to "begins with P", hinting at a pseudonym, wot dun it.
So! let's have a bit of

MINERAL

.