Yes it's a convenient timebase.
Yes, it doesn't have all the outputs brought out because there aren't enough pins! The designers decided that it was important to have 14 division stages, and they only had 10 pins available for outputs on the 16-pin package (after allocating VDD, VSS, reset, and three pins for the oscillator). At the time the 4060 was designed, few ICs had more than 16 pins. They chose the outputs they thought were most important or useful, I guess.
The CD4020 is similar, without the oscillator. It also has several outputs missing. The CD4040 is a 12-stage counter with all outputs brought out. It doesn't have an oscillator, just VDD, VSS, clock in, and reset, so there are 12 pins available for outputs. There's also the CD4024.
Any flip-flop that can be configured as a T flip-flop ("toggle"), i.e. a divide-by-two stage, will work. You can use a 4027, or a 4013 with its D input tied to its Q-bar output.
Yes I have used a 32768 Hz crystal with the 4060. The capacitor values are calculated in the normal way for a Pierce oscillator using an inverter. Take the specified load capacitance of the crystal (usually 6 pF or 12.5 pF for these crystals), double it, and subtract a few pF to cover stray capacitance and gate input capacitance, and use the resulting value for both capacitors. For example if the load capacitance is specified as 6 pF, I would use two 10 pF or 8.2 pF capacitors.
You also have to be careful with the resistor values. Watch crystals have to be driven at quite a low power. The resistor from the gate output to the crystal needs to be quite high. I think I used 100k. The gate bias resistor (across the crystal) should be as high as possible; 10M is good.