Mode-locked pulse outputs with switchable single/dual wavelengths and widely tunable spectral bandwidth are demonstrated by fully exploiting multiple soliton formation mechanisms combining single-wall carbon nanotube, intracavity loss tuning and nonlinear polarization rotation. An isolator with single-polarization fiber pigtails is additionally inserted in a ring fiber laser cavity to introduce polarization-dependent loss modulation for gain profile tuning and nonlinear polarization rotation. Mode-locked by a home-made single-wall carbon nanotube saturable absorber, switchable single/dual-wavelength pulses centered in the 1530- or/and 1550-nm gain regions of erbium-doped fiber are experimentally observed by tuning the intracavity loss to tilt the gain profile. Moreover, the spectral bandwidths of single-wavelength pulses centered in the 1530- and 1550 nm regions could be continuously tuned from 2.4 to 4.0 nm, and 2.7 to 9.0 nm, respectively. Such widely tunable spectral bandwidths are attributed to hybrid mode-locked mechanisms combining the nonlinear polarization rotation and single-wall carbon nanotube. Our results give a deep insight into the well-controlled gain profile tuning and provide a relatively simple setup and method to obtain bandwidth-tunable, wavelength-switchable pulse outputs, showing the potential to meet various requirements of ultrafast laser applications.