We present Generalized Gradient Corrected Density Functional Theory (DFT) calculations of the static and dynamic properties of stage-I potassium and potassium-ammonia graphite intercalation compounds KC8 and KC24(NH3)(x), with x = 0, 1, 2, 3, 4, 4.5, 5. For each system, a full geometry optimization was carried out, and finite temperature first-principle molecular dynamics (FPMD) simulations were performed on a selected number of compounds (KC8, KC24, KC24(NH3)(4), and KC24(NH3)(5)) in the temperature range 373-573 K and overall simulation times of 2-4 ps. K was found to adsorb preferentially above C-6 rings and, typically, to diffuse parallel to the ab-plane at finite temperature. In addition, a slow oscillatory motion perpendicular to the carbon layers was observed, with K residing in turn closer to one or another carbon plane. We speculate on these findings in their connection with the electronic properties of potassium-ammonia intercalates in the vicinity of the metal-nonmetal transition at x similar or equal to 4.3.