Point the axis at the centre. The acceleration in circular motion is radial — resolve forces along the radius (toward the centre) and along the tangent, never along horizontal/vertical.
Centripetal is a role, not a force. Write ΣFradial = mv²/r and let tension, gravity, friction or the normal fill that role — do not add a separate "centripetal force".
Centrifugal only in a rotating frame. Sitting on the turning body, add the pseudo-force mω²r outward; in the ground frame it does not exist.
Uniform ⇒ speed constant, velocity not. Even at constant speed the direction turns, so there is acceleration v²/r toward the centre.
Speed changing ⇒ add a tangential kick. Then at = dv/dt runs along the path and the true acceleration tilts forward off the radius — see §04.