Extruded heatsink question
Q1: (theoretical question) if I apply a single TO-220 in the middle of such heatsink long 20cm, can I consider it to have a Th of 10°C/W?


Yes, but remember that that's the temperature rise of the heatsink. The component mounted on it will have thermal resistance to the heatsink and the chip inside the component will have thermal resistance to it's case. These all add to the chip temperature rise and will be higher than the heatsink temperature.


  Q2: (theoretical question) if I cut it in half along its extrusion dimension, I have (roughly) 2 heatsinks of 20°C/W each long 10cm?


That would be the expected result.


  Q3: What about the heatsink in the link? Can I use it with a single, "small" TO-220 and pretend to have around 3°C/W?


We don't really pretend in this business. The specification is 3.03°C/W so it looks OK.

For a full thermal analysis you need to sum all the thermal resistances and calculate the temperature rise for a given power flow. This is similar to Ohm's law. See the first link below.

Table 1. Comparison between electrical and thermal resistance calculations.

Electrical                                    Thermal
Voltage (potential difference) [V]            Temperature difference [K] or [°C]
Current [A]                                   Heat flow (power) [J/s] = [W]
Electrical resistance [Ω] = [V/A]             Thermal resistance [K/W] or [°C/W]


Links: 


Calculating heat sinks.
Understanding
Thermal
Dissipation
and
Design
of
a
Heatsink.