Yes (although its a little small for old eyes :-)) the schematic for the switches looks correct. A 10 ohm pull up resistor would technically work but it will draw too much current. A 1k or even 10K resistor would be a more reasonable value (value isn't all that important if they are high enough, if you already have 2.2K resistors they would work fine).
I was going to say the LCD is wrong, but then I looked more closely at the schematic and see that they have tied the write line high (so it never reads) which will indeed work and saves a pin so that should work fine (I did find it very odd that there would be an error on the Arduino site 
).
As to the motor driver pins, yes they all need to be connected to either power or ground usually through a pull up or pull down resistor like the push buttons but a direct connection to ground or +5V if they need to be high will also work. In general CMOS inputs (and most stuff you will use is CMOS these days) should not be left to float (unconnected). They must be connected to either ground or vcc (3.3 or 5V typically) as noted usually via a 1K ohm resistor.
In this case without the enable pin being tied to ground (also known as tied low in case I slip and use that term) the motor driver won't do anything as it is not enabled. Similarly the slp (sleep) pin must be tied high or the chip will go to sleep and not function. The reset pin needs to be either driven from an Arduino data pin (if you want to be able to reset the motor driver board) or tied to +5v (or through a pull up resistor to 5v) so the chip won't be in reset and not function. The ms1/2/3 pins control step size setting them all to 0 will (from the data sheet I haven't actually done this) cause it to take full steps and yes the means connecting them to ground, if you want microstepping for better resolution you would need to connect them to Arduino pins (and find the Arduino microstepping library, I'm pretty sure there is one).
One last thought is power to the stepper motor. Steppers are generally high current devices. That means they will tend to flatten your batteries fairly quickly. I'm assuming you have wall wart
power for the Arduino, you may want to consider replacing the batteries with a 6V wall wart (with a current rating appropriate for the stepper motor) to save battery cost. The batteries should work fine, they just may not last all the long.
Peter Van Epp