We present a systematic angle-resolved photoemission spectroscopic study of the high-Tc superconductor class (Sr/Ba){1-x}(K/Na)xFe2As2. By utilizing a photon-energy-modulation contrast and scattering geometry we report the Fermi surface and the momentum dependence of the superconducting gap, Delta(k). A prominent quasiparticle dispersion kink reflecting strong scattering processes is observed in a binding-energy range of 25-55 meV in the superconducting state, and the coherence length or the extent of the Cooper pair wave function is found to be about 20-angstrom, which is uncharacteristic of a superconducting phase realized by the BCS-phonon-retardation mechanism. The observed 40 meV kink likely reflects contributions from the frustrated spin excitations and scattering from the soft phonons. Results taken collectively provide direct clues to the nature of the pairing potential including an internal phase-shift factor in the superconducting order parameter which leads to a Brillouin zone node in a strong-coupling setting.