Solution to the first wave of puzzles

Each of these revealed a line of cipher which appears to have been written by Moray and discovered by Dupin, who sent them to Grandison Senior, Mr Grandison's grandfather. The lines deciphered spelt out a message which can be seen in the Unearthed So Far section of The Gold-Bug website.

The solutions to my puzzles were as follows :)

the second line
Captain Kidd, as according to Poe's story

the third line
The obelisk outside the Temple of Luxor is the twin of that now in Paris in Place de la Concorde

the fourth line
the message is written along the diagonals starting in top left corner T, then H-E, etc yielding THE LAST WORD FOUND IN READING THIS DIAGONAL INSCRIPTION

the fifth line
The narrator of Poe's story, whom we now know to have been Moray, notes Swammerdamm in the third paragraph of the original story.

the sixth line
The wise man's route traces out the symbol of infinity.

the seventh line
It's a substitution cipher whose keyword is CHEST which deciphers to WHICHEVER IS THE KEYWORD IN THE ENCIPHERMENT OF THIS SENTENCE IS THE ANSWER YOU NEED