1. Two things. You can use clamp diodes, e.g. BAT54S is very common (or something smaller if capacitance is critical), so the input doesn't exceed the power rails by much.
In either case (clamp diodes or TVS), the voltage will still spike beyond whatever the nominal 'catch' voltage is (due to ESR and ESL), so you add some series resistance between TVS/clamp and the IC.
That way, instead of a 2kV ESD spike going into the chip (probably all it's rated for, if that), you can get an 8kV spike going into the circuit, which is attenuated by the outer TVS/clamp to maybe a 50-100V spike. The trick is, if you connected *that* directly to the pin, it would be almost as bad as no TVS at all, because that 50-100V spike now has a very low impedance. So you add a series resistor to let the IC's clamp diodes fill in the rest.
Any resistance is better than none, but 10-100 ohms for digital or non-precision analog outputs, or 100-10k for inputs, is usually good.
Oh, and don't forget ESD applies to inputs and outputs. Just because it's driving a signal doesn't mean it's any more robust than the rest.
As a bonus, you can add a cap to ground after the resistor (for inputs), which accomplishes some filtering. Or for resistors under 100 ohms, a ferrite bead may be helpful too. Good for EMC.
2. Avalanche TVS are just big fat zener diodes rated for peak currents, so you could use them for clamping inputs (casually) or regulating supplies. But I wouldn't recommend it.
For inputs, you can make excess-voltage-tolerant inputs by adding series resistance in front of the TVS. The resistor will probably arc over under ESD conditions*, so you can't count on it to bear anything under that condition, but under DC conditions, a hundred volts on a high enough resistor value, sure, do that all day no problem! (You also get a little implicit EMC filtering, because the TVS/clamp has some capacitance, which the resistor works against as a filter.)
Note that the input equivalent circuit changes depending on what voltage you apply, so it's no longer just a resistor and a pin capacitance kind of equivalent, but there's diodes and clamps and stuff in there. If you need a very consistent input (e.g., oscilloscope 50 ohm / 1M + 20p matched), you'll want to consider the input circuit in more depth.
For protecting supplies, yes you could use a TVS as a regulator diode, but I would much rather suggest a proper method, like an LDO to ride out the swell plus a low voltage MOV to absorb the energy (e.g., automotive load dump), or a thyristor type TVS (or one of your own fashion) to crowbar the input.
*One example offhand:
http://seventransistorlabs.com/Monitor/Images/NeckBoard2.jpgNo idea if the 22.0 ohm 2W? resistors are, like, HV or arcover-prevention rated or something, but they certainly had some idea what they were doing here. The problem with a CRT is, sometimes the high voltage arcs over internally (which would be equivalent to something like 30kV machine model -- NOT a kind discharge!), and that needs to stay away from the >100MHz bandwidth video amplifier: low capacitance, high precision, very sensitive!
What they do is, neon tubes (they're probably not actually plain old NE-2, but GDTs that happen to be made in that style) clamp the brunt of the spike, probably still passing a few nanoseconds over a thousand volts -- GDTs don't turn on instantly. The resistors absorb this remainder, and some low capacitance diodes near, or inside, the amplifier handle the rest. The amplifier internally is probably bipolar, so it won't be extremely ESD sensitive, but it will be made from small enough bits that it still needs protection against that remainder (I didn't get a picture of what parts are under the heatsink, and there are generic SMTs on the bottom side, but I think there are additional clamp diodes in there).
Tim