Scribe Ineti said:
1. If you wanted to play a tragic hero, how would you present it to the GM? How would you role-play such a character?
Ahh, my favorite kind of hero.
I am not sure how to answer your questions-
a. The same way I pitch any character I plan. Though, to be honest, I always try to throw some tragic flaw in every character- the moments of heartbreak are not to be missed.
b. It depends on the character- tragic heroes can still be people who have a good laugh, but almost all of them have the tragedy of their past constantly on the edge of their minds.
example 1:
I played a LN fighter who was in love with sister of the king he had sworn to protect. While she loved him in return, noble law required she marry another noble- and she was betrothed to another player in the group.
The fighter eventually sacrificed himself to close a demonic gate- was cursed with immortality.. watching his world age and be taken over by demons.
He was a kind and generous person, but the time always slinked away during times of celebration to hold the handkerchief of hers in his possession.
example 2: Al qadim thief who became tragic- he found/married and had a child with his soul mate, but she could not abide by him adventuring and making enemies of the world - she left him and took their son.
He was still a dashing swashbuckler who made "witty" remarks, but he also became an alcoholic.
2. If you were a GM, and wanted a tragic hero type or had a player ask to play a tragic hero, how would you go about it?
I absolutely love it, but it is best handled slowly.
I stretch it out and only use bits of the tragedy as it slowly catchs up with them- until the moment of destruction/triumph is at odds.
Along these lines, I also take a clue from the 7th Sea rpg. I ask the players to tell me how they envision their characters being killed. I tell them it doesn't mean their character will definitly die this way.. or not die another way, but during a situation similar to what they describe.. the dice fall as they will.
Why do this?
1) You get a heck of a good idea how they imagine their character growing and the type of challenges the would like to see for their characters.
2) You give the players a bit more control over their characters destiny.
3) You have a great way to raise tension.
Example: A character imc is a fighter/rogue who likes to scar people he defeats in combat (with a scar under each eye as if they were crying).
His characters background had the son of a military/noblemen general .. err.. taking advantage of his char's love. In revenge, he challenged him to a dual - and did the scars. The son is now known as the "crying prince", which has angered a lot of people in that family. It also led to him being disowned by his own family.. forcing him to flee to the seas.
He envisions his character dying in some dramatic final battle with the crying prince.
As the dm, I am slowly working this into the story- the general has hired pathetic assassins to kill the character. And a npc he has spent a lot of time woo'ng is secretly the sister of the prince- who will eventually betray one of them.
In the end, I would not force anyone to play a tragic character, but would definitly encourage anyone who shows interest.
I think the final key is that a tragic character has to have some kind of tragic end- not necessarily a bad ending to the character.. but one that holds some degree of tragedy. A happy ending just betrays the whole point.

(I must stop before the examples start to flood again..)
You mention you plan to start a new campeign- why do you ask? Do you have a player interested?
Good luck!
FD