1) What planet is the homeworld of the Quarren?
It is called Dac by the Quarren, otherwise known as Mon Cala by Dac off-worlders.
1a) Name one sentient species they share their world with
Mon Calamari are the most widely travelled throughout the galaxy and therefore the most widely known.
2) What species was Ki Adi Mundi?
Cerean.
3) Who did Qui-Gon Jinn win Anakin Skywalker from?
Watto the Toydarian.
3a) What was the name of the event that this happened at?
A pod race called the Boonta Eve Calssic.
4) What species was Jabba the Hutt?
Jabba the Hutt, was a Hutt.
5) What does Nal Hutta translate to in Basic?
Glorius Jewel.
5a) What was the name of its moon?
Nar Shaddaa.
6) Who was the Sith Apprentice during Episode II?
Darth Tyranus was the appretice of Darth Sidious in Episode II.
7) How did Obi Wan Kenobi "die" during Episode IV?
Darth Vader used a fairly poorly executed left-to-right Djem So (Form 5) central sweep to kill Obi-Wan Kenobi.
While it's true that Vader's form had deteriorated in his later years as a result of having no true opponents to test himself against,
the rumours circulated by Jedi scum that Obi-Wan had voluntarily sacrificed himself to the Force are laughable.  
8) Who blew up the Death Star at Yavin?
Luke Skywalker got off a lucky shot with a couple of proton torpedoes.
8a) Name one person that assisted him and survived the space battle
Wedge Antillies was in the trench with Skywalker. He survuved because he like a coward from the battle.
9) How did Jabba's slave girl, Oola, die?
She was eaten by Jabba's pet rancor.
10) What planet was Mon Mothma from?
Chandrila ot eh Bormea sector.
11) What happened to the rebel medical frigate at the Battle of Endor?
According to official fleet records the medical frigate Redemtion was destroyed by the second Death Star, this is not actuially seen in the holos released after the battle however and the4refore I assume it is propaganda.
12) Who was Boba Fett's "father"?
Jango Fett was the genectic progenitor of Boba Fett.
12a) Who killed him?
Jango Fett was beheaded by Mace Windu as he attempted to protect his son, Boba, during the battle of Geonosis.
13) Name one Imperial officer force choked to death by Darth Vader during Episode V
Admiral Kendal Ozzel was summarily executed for grosss incompetence by Darth Vader
13a) Name another Imperial officer killed that way in Episode V
Admiral Piett, Ozzel's equally incompetent successor.
14) What color was Darth Mauls lightsaber
Classic, beautiful red.
15) Where is the rebel base?
Dantooine, wait, no that's not right, Yavin 4, then Hoth. (But I'm pretty sure there was an encalve on Alderaan too.)