l. The writer means that he inherited all these advantages from an affluent, privileged family, the sort of family that would stipulate which heir received which tea service.
2. Right. The nicknames indicate just how close and cozy he will be with all sorts of important people.
"Fast comeback at the front stairs". The French have a term, "staircase wit" meaning you think of the ideal retort as you are leaving the party. In this ideal world, he'll have his snappy comebacks ready to deliver as he enters the social whirl.
He doesn't look down on authority. He wants to be one of the powerful.
I'm guessing "re-Columbus" would be "re-discover" us.
3. He wants his stocks and other investments to appreciate magnificently in the most favorable of markets..
In the Stock Market "Bulls" are "Buyers" and a Bull Market is one that is full of opportunities for investors. He's invoking all sorts of opportunities for his happiness and success as well as financial triumphs.
4. Here "wag" means a joking friend, even a practical joker.
Lyrics for "The Girl from Ipanema":
http://bossanovaguitar.com/antonio_carlos_jobim/chords_lyrics/the_girl_from_ipanema.html
Good luck.