This paper investigates connectivity-preserving formation control for high-order multi-agent systems under switching distance-dependent topologies, actuator faults and external disturbances. The admissible interaction edges are selected by a switching signal, while the actual edge weights vary continuously with inter-agent distances. To avoid unsafe jumps of algebraic connectivity at switching instants, a connectivity-certified switching condition is introduced. Between switching instants, an algebraic-connectivity-dependent barrier signal is incorporated into a recursive formation controller. A fixed-time extended state observer is designed to estimate the matched lumped uncertainty caused by actuator loss of effectiveness, additive faults and external disturbances. Explicit ultimate estimation-error bounds and a fixed convergence-time upper bound are derived. The effects of command filtering and smooth actuator saturation used in the numerical implementation are further represented by bounded implementation residuals in the stability analysis. Theoretical results establish boundedness of all closed-loop signals, uniform ultimate boundedness of formation errors and preservation of a prescribed connectivity margin under the stated hybrid safety conditions. Numerical simulations with five planar followers illustrate formation tracking, connectivity preservation, fault-tolerant disturbance rejection and observer estimation performance.