Breaking the conventional stereotype that ferroelectrics are necessarily insulating, two-dimensional (2D) ferroelectric metals combine seemingly incompatible switchable electric polarization and metallic conductivity, providing a fertile ground for the discovery of novel electrical transport phenomena and the development of innovative electronic devices. Using the semiclassical Boltzmann equation and first-principles calculations, we systematically investigate the linear and nonlinear transport responses of the intrinsic 2D ferroelectric metal PtBi2 to an applied electric field. Our ab initio molecular dynamics simulations reveal that it possesses a high Curie temperature reaching 800 K. We propose that the crystal structure of its high-temperature paraelectric phase can be explicitly distinguished through simple measurements of the in-plane electrical conductivity. Quantitative calculations of the Edelstein effect and the intrinsic spin Hall effect demonstrate a sizable charge-to-spin conversion efficiency, highlighting its potential in spintronics. We also find that a Berry curvature dipole-induced nonlinear Hall effect emerges in uniaxially strained PtBi2. Furthermore, we highlight the unique advantages of 2D ferroelectric metals in gate-controlled transport applications. Based on the domain wall scattering mechanism, we conceptually design a novel ferroelectric metal field-effect transistor (FEM-FET) capable of nonvolatile switching between high-resistance and low-resistance states under a gate voltage. Our work not only unveils the rich transport physics in 2D ferroelectric metals but also provides valuable insights into the design of next-generation nonvolatile memory and spintronic devices.