How long can Legionella survive at 60°C?
Usually cell death would follow first order kinetics.

$$X=X_0e^{-kt}$$

where $X$ is the number of cells at time $t$, $X_0$ is the initial number of cells and $k$ is the death rate constant. You can get the constant by solving for 90% reduction in 2 minutes. Then just substitute and get the time required for 99.99999% reduction — 10 minutes.

For your follow up questions, see the same wikipedia article. 


  Moist heat sterilization (superheating to 140 °F (60 °C) and flushing)
  is a nonchemical treatment that typically must be repeated every 3–5
  weeks.


It also depends on how much is the bacterial load in the input. 

Other sources (Farhat et al. 2012; Whiley et al., 2017) suggest 70°C treatment for 30 minutes.

However, Legionella has been shown to survive heat treatment of 70°C/30min (reviewed by Whiley et al., 2017). Legionella can also be "protected" by other micro-organisms such as certain types of Amoeba, in the water.

So, probably multiple levels of disinfection is needed.