Correct.
And I thought cricket was confusing! ;)
An inning can go on indefinitely, you could score any number of runs. So the bottom of the ninth is the last chance the losing team has to make up the runs to win the game.
If the winning team bats in the bottom half of the inning and they lead when the bottom of the ninth comes up they skip it, since the pitching team can't do anything to change the result of the game.
The bottom of the ninth usually has the entire crowd standing (since the home team always bats in the bottom and they are trying to come back and win) and is a very exciting time.
Inside-Outside is used instead of left-right because batters can be left or right handed, and it is more important to note if the ball is heading toward the player or away.
Pitching inside has value, as it is hard to hit a ball hard when it is closer to your hand, but you have the chance of actually hitting the batter, which gives the batter a free base.
… because they're on their way to their cars to beat the traffic out of the parking lot before the game is actually over. 
Okay, it's getting clearer.
Nine innings sounds like a really long game!
Hence the hotdogs and the beer.
Yeah, but you can grab those whilst doing something entertaining instead… 
At least it doesn't last FIVE SODDING DAYS.
I was a football (soccer) fan as a kid. 90 minutes is a sensible number, with a nice break in the middle.
I tried watching American football once. It took about six years to play five minutes of game.
I find American football a lot like cricket - often when very little appears to be happening, one team has is doing something very well but you need to know the sport to see and understand it. They've wonderfully tactical at the top level, whilst relying on contests between individuals underneath
I believe if you cut out the time at the line of scrimmage, and go with just snap of the ball to whistle and cut all the time inbetween, the actual action of an American Football game is around 11 minutes, and takes about 3 hours and 11 minutes to play.
As for Baseball the average MLB game is 3 hours, and a decent bit of that is TV time. A non-televised game takes a lot less time, in college I would work the games and it was usually 90 minutes.
Americans like talking about Sports even more than we like watching or playing them, so we need big breaks in the action.
That's why they play 162 games, to make up the time.
The flipside of that is the time leading up to the snap is about working out the opposition - I was the team photographer for my local team in London (amateur) and the things that the youth team players on the sideline watching the game could pick out was incredible. They were half my age and I felt like a toddler trying to keep up with the things they were observing. Actually listening to those lads did a lot to help me appreciate the importance of formation in football (soccer)
It's all the stopping and starting I couldn't stand. Just as things were starting to get vaguely interesting after a couple of seconds of play, we had to listen to people talking about it for 5 minutes whike everyone moved around.
It just seems so weird to a soccer fan to have the game essentially "reset" so often.
Yeah, I get that - I don't know if I would have kept watching the game if it hadn't been for Bloodbowl! Well, and the Cheerleaders who were very impressive to a twelve year old boy...
I was also lucky in that a friend's dad was a fan and we had a little ball we threw around outside as kids
Time for the obligatory Simpsons' video highlighting the difference in countries perceptions of certain sports.
https://www.youtube.com/watch?v=qjp1Zrvn8VQ
I'm a soccer and football fan, and the difference between the posturing and bluffing strategy of Football and the flowing emergent strategy of Soccer is really interesting.
I didn't like Baseball until I got really into the history of the Samurai of Japan, and studied sword forms for a while. Baseball is really a constant set of duels, and the story of each at bat is really fascinating.
I love the study of ones opponent, and the attempt to quantify every part of the game, it is really fascinating stuff for me.
It is also a lot of fun drinking a beer and taunting the other team's left fielder while it's warm and the sun is setting behind the gorgeous skyline PNC park gives a great view of.
That's another thing that's weird to me coming from a soccer background - drinking beer at a game.
Have you tried Cricket? That has a similar duel aspect to baseball (between bowler and batsman), but field placement forms a part of it too with some positions left empty to tempt particular shot attempts, with other positions occupied to capitalise on a misjudgement. That said, I don't know how much of that can be observed in the more digestible forms of the game (the 50 and 20 over versions) as they have fielding restrictions for a certain number of overs
You can go crazily stats nerd with batsmen vs certain types of delivery too!
EDIT: There is a book called "Inverting the Pyramid" that was a fascinating read, giving the history of the tactical eveolution of soccer from 2-3-5 to 5-3-2 (and beyond)
Just wanted to second that Inventing the Pyramid is a fantastic read