  Understanding the origin of fast radio bursts (FRBs) has become the main
science driver of recent dedicated FRB surveys. Between July 2019 and February
2022, we carried out ALERT, an FRB survey at 1370 MHz using the Apertif
instrument installed at the Westerbork Synthesis Radio Telescope (WSRT). Here
we report the detection of 18 new FRBs, and we study the properties of the
entire 24 burst sample detected during the survey. For five bursts, we identify
host galaxy candidates with >50% probability association. We observe an average
linear polarisation fraction of $\sim$43% and an average circular polarisation
fraction consistent with 0%. A third of the FRBs display multiple components.
The sample next reveals a population of highly scattered bursts, which is most
likely to have been produced in the immediate circumburst environment.
Furthermore, two FRBs show evidence for high rotation measures, reaching
|RM|>$10^3$ rad m$^{-2}$ in the source reference frames. Together, the
scattering and rotation measures ALERT finds prove that a large fraction of
FRBs are embedded in complex media such as star forming regions or supernova
remnants. Through the discovery of the third most dispersed FRB so far, we show
that one-off FRBs can emit at frequencies in excess of 6 GHz. Finally, we
determine an FRB all-sky rate of $459^{+208}_{-155}$ sky$^{-1}$ day$^{-1}$
above a fluence limit of 4.1 Jy ms, and a fluence cumulative distribution with
a power law index $\gamma=-1.23\pm0.06\pm0.2$, which is roughly consistent with
the Euclidean Universe predictions. Through the high resolution in time,
frequency, polarisation and localisation that ALERT featured, we were able to
determine the morphological complexity, polarisation, local scattering and
magnetic environment, and high-frequency luminosity of FRBs. We find all these
strongly resemble those seen in young, energetic, highly magnetised neutron
stars.
