The neutron star transient and 11 Hz X-ray pulsar IGR J17480-2446, recently discovered in the globular cluster Terzan 5, showed unprecedented bursting activity during its 2010 October-November outburst. We analyzed all X-ray bursts detected with the Rossi X-ray Timing Explorer and confirmed their thermonuclear origin, despite the fact that many do not show the canonical spectral softening along the decay. The burst energy, peak luminosity and daily-averaged spectral profiles all evolve smoothly throughout the outburst, in parallel with the persistent (non-burst) luminosity. We also find that the peak burst to persistent luminosity ratio determines whether or not cooling is present in the bursts from IGR J17480-2446, and we compare these findings with X-ray bursts from other rapidly accreting neutron stars. We conclude that the detection of cooling along the decay is a sufficient, but not a necessary condition to identify an X-ray burst as thermonuclear. We also discovered milli-hertz quasi-periodic oscillations near the outburst peak, which smoothly evolve into a rapid series of faint bursts as mass accretion rate decreases. Finally, we explore the influence of spin and magnetic field on the unique bursting properties from IGR J17480-2446.