  We present a detailed theoretical investigation of transport through a
single-walled carbon nanotube (SWNT) in good contact to metal leads where weak
backscattering at the interfaces between SWNT and source and drain reservoirs
gives rise to electronic Fabry-Perot (FP) oscillations in conductance and shot
noise. We include the electron-electron interaction and the finite length of
the SWNT within the inhomogeneous Tomonaga-Luttinger liquid (TLL) model and
treat the non-equilibrium effects due to an applied bias voltage within the
Keldysh approach. In low-frequency transport properties, the TLL effect is
apparent mainly via power-law characteristics as a function of bias voltage or
temperature at energy scales above the finite level spacing of the SWNT. The
FP-frequency is dominated by the non-interacting spin mode velocity due to two
degenerate subbands rather than the interacting charge velocity. At higher
frequencies, the excess noise is shown to be capable of resolving the
splintering of the transported electrons arising from the mismatch of the
TLL-parameter at the interface between metal reservoirs and SWNT. This dynamics
leads to a periodic shot noise suppression as a function of frequency and with
a period that is determined solely by the charge velocity. At large bias
voltages, these oscillations are dominant over the ordinary FP-oscillations
caused by two weak backscatterers. This makes shot noise an invaluable tool to
distinguish the two mode velocities in the SWNT.
