As I understand it, the zener diodes are meant to clamp the lines to a maximum voltage (5.6V in this case) to protect the devices on the bus, and is especially useful for long i2c transmission lines. Is my understanding correct?
This is probably correct, but without knowing where you got the circuit from, it's difficult to know exactly what they had in mind. Since the zener voltage is 5.6 V and the I2C pull-up voltage is 3.3 V, the zeners will have no effect on the circuit in normal operation.
Even on a 5 V I2C bus, the zeners would have no effect in normal operation.
Do I need clamping diodes if all of my i2c slave devices are on the same board, relatively close together?
Very likely, if everything is on the same board, you can simply omit the zeners.
What do the series resistors do, and do I need them?
In the original circuit, the series resistors were probably used to limit the current flow through the zeners in an over-voltage condition.
If you decide you don't need the zeners, you probably don't need these resistors, either.
The battery gauge IC allows up to 6V on its SDA/SCL pins, so is it ok to pull the bus up to 3.3V, even though the gauge is running at 2.5V?
Would it be better to level shift them to 2.5V?
I agree with your reading of the datasheet on this. Input high voltage levels from 1.2 to 6 V are allowed for these signals on this chip. Therefore there's no need to do any level shifting at all --- simply use 3.3 V pull-up for your I2C bus.
The accelerometer address is 0x1D by default and can be changed to 0x1C with a bit of soldering(Found in the Address Select Jumper section of the guide you linked). The gyroscope address is 0x69 by default and can be changed to 0x68(Found in section 6.1.1 of the datasheet, and the I2C Address Jumper section of the guide you linked). The Arduino can theoretically support as many I2C devices as can be acquired without having two that share an address.
Note also that accelerometers and gyroscopes are often packaged together on a single chip, which may be easier to work with. I've used the MPU-9150 with good results.
Best Answer
The I²C bus pullups and VLOCGIC on the MPU chip must be connected to the 1.8 Volt rail:
simulate this circuit – Schematic created using CircuitLab
The MPU-6050 still needs 3.3 Volts on its VDD pin. Note that this will only work if your MPU-6050 module has not connected VLOGIC to VDD in any way on the PCB.