I have no idea what "grind Faction rep" means.  Is that an MMO term?

It's a term made popular by WoW. Faction rep is just another boring time sink employed by these developers to artificially increase re playability by adding an independent (from level) progression meter. So, in certain cases you kill one one testicled jackal; and gain +10 rep out of say, 40,000 you need to get to the max rep level and get that piece of marginally better gear.

That's why I get bored of them quickly. I will play WoW every once in a while with my brother, but I get bored of it for a few months. Kind of a waste to pay $15/month just to play every once in a while.

Now for some info on the connection to the previous games:

How does Star Wars: The Old Republic relate to Star Wars: Knights of the Old Republic?
 
Star Wars: The Old Republic takes place approximately three hundred years after the events of Star Wars: Knights of the Old Republic (KOTOR). At the conclusion of the Jedi Civil War in KOTOR, Revan disappeared into unknown space in search of a great threat to the Republic, an expanding Sith Empire led by a mysterious Emperor who planned vengeance for his ancient Jedi enemies. Revan never returned from unknown space, but the Sith Empire did, kicking off a war with the Republic that lasted for decades. Now, despite the uneasy truce created by the Treaty of Coruscant, the tension among the divided star systems is threatening to once again tear the galaxy apart.

Hmm, so the greater threat was just more sith? Kind of disappointing.

Will I see any characters from Star Wars: Knights of the Old Republic?
 
Given that it is approximately 300 years since the events of Star Wars: Knights of the Old Republic, many of the characters have passed away. However, their legacy does live on as many of their descendants will be part of Star Wars: The Old Republic. Some droids can last a long time as well.

I wonder if we'll see T3-M4?

I am curious as to how they plan to accomplish the fact that your actions supposedly affect the plot. How will you interact with other players, if they may have made other choices? How can you play along with them if their story is different?

Ohhh... I didn't remember that.

http://starwars.wikia.com/wiki/Sith_%28species%29
I guess they were the original inhabitants of Korriban.

everquest had 100x as much rep grind as wow, saying wow popularized the term is kind of misleading

Everquest may have had more of it, but I can guarantee you WoW made this annoying little mechanism far more well known than it was back in the old days.