Results of a detailed investigation of the ferromagnetic superconductor UGe 2 using positive muon spin rotation and relaxation techniques are presented. The pressure and temperature dependences of the frequencies and related spin-spin relaxation rates show that the transition from the weakly to the strongly polarized magnetic ͑WP-SP͒ phases is still observable at T X Ӎ 3 K under a pressure of 1.33͑2͒ GPa. Thus this transition survives at higher pressures than previously believed. The temperature T X at 1.00͑2͒ GPa corresponds to a thermodynamic phase transition rather than a crossover. No such statement can be given reliably at lower pressure. A substantial shrinking of the component along the easy axis of the diagonal hyperfine tensor, at the muon site where it is large, is observed in the SP phase relative to the WP phase. This corresponds to an appreciable decrease in the electronic density at the Fermi level in the SP phase. The investigation of the paramagnetic-ferromagnetic critical spin dynamics at ambient pressure and at 0.95͑2͒ GPa shows that the simple one-band model is an oversimplification inconsistent with our critical spin-dynamics results. Data from specific heat, Fermi-surface studies, Hall effect, neutron form factor, and spectroscopic techniques supports this conclusion. Even at 0.95͑2͒ GPa the conduction electrons are characterized by a small magnetic moment, relative to the bulk magnetization per uranium atom.