ADC: should I pull up the unused pins?
First, read the data sheet and the application notes. Carefully.

Generally any unused outputs can stay unconnected. If an apparently unused output needs to stay connected to some source of bias for proper operation of the rest of the chip, then the data sheet will tell you.

Generally all digital inputs need to be connected to a valid logic level to avoid excess supply current, even if you won't be using the function it's driving. If an input has an internal circuit to hold it at a valid level, then the data sheet will tell you that it can be left open.

Generally any unused analogue inputs should be kept within their valid voltage range, and quiet. Study the data sheet for each input to see what the valid range is, whether it will stay within that if left unconnected, and whether power consumption is dependent on its voltage. Ground is often OK. 

In professional equipment, unused inputs are often taken to specific voltages through a series resistor. This allows the input to be probed during test, which allows standard test programs to be used. This is not usually an issue for hobby designers.