Yeah it's tough to really gauge how even a "battle" would take place against the wall like that... The Giants seemed like their best hope to breach it. Guys climbing up the face on ropes seems... hopeless to me, but it's fiction so who knows. I liked what they had for those guys. Wow.
Giants, Mammoths, and all that stuff add a variable to the whole thing though that was kind of unpredictable.
I didn't know that about the Castle Black walls (never read the books obviously), so that explains how the walls are pretty much easily breached without even a ladder.
Ygritte said about the guys on the wall being "leftovers" (I think that's what she called them), so yeah the guys there seemed like the guys too worthless to have above.
I imagine fights within a castle's walls would've opened up into chaos... That's seemingly the case what I've read of them. You either stop the invaders at the wall, even at a wall's breach, or usually you're screwed and organized defense just goes out the window. Of course that's traditional sieges... Which usually have a massive army outside waiting to get in, too.
Troop movements don't mean much in those situations... Castles usually had layered defenses, and as things wore down the troops just moved to the next layer back. Towers in castles were designed to be islands of opposition even when the walls around the towers would fall. So there's some tactics there, but like Nick said it seems Castle Black wasn't given much defensibility facing south, so it just goes to **** more or less.

Though it makes for a lot more fun thing to watch than potentially months upon months of siege warfare.

It seems like the truly more traditional medieval battles like Rob Stark's campaigns were glossed over, possibly because they'd really not be as visually stunning as things like Blackwater, or The Wall... Guys marching around in formations jabbing at one another with super long spears, always trying to just wheel around and outflank/maneuver the other 1000 guys while big groups are standing around in reserves and other groups are just launching hails of arrows and stuff.