  Starting from the paradigmatic spin-boson model (SBM), we investigate the
static and dynamical properties of a system of two distant two-level emitters
coupled to a one-dimensional Ohmic waveguide beyond the rotating wave
approximation. Employing static and dynamical polaron Ans\"atze we study the
effects of finite separation distance on the behavior of the photon-mediated
Ising-like interaction, qubit frequency renormalization, ground-state
magnetization, and entanglement entropy of the two-qubit system. Based on
previous works we derive an effective approximate Hamiltonian for the
two-impurity SBM that preserves the excitation-number and thus facilitates the
analytical treatment. In particular, it allows us to introduce non-Markovianity
arising from delay-feedback effects in two distant emitters in the so-called
ultrastrong coupling (USC) regime. We test our results with numerical
simulations performed over a discretized circuit-QED model, finding perfect
agreement with previous results, and showing interesting dynamical effects
arising in ultrastrong waveguide QED with distant emitters. In particular, we
revisit the Fermi two-atom problem showing that, in the USC regime, initial
correlations yield two different evolutions for symmetric and antisymmetric
states even before the emitters become causally connected. Finally, we
demonstrate that the collective dynamics, e.g., superradiance or subradiance,
are affected not only by the distance between emitters, but also by the
coupling, due to significant frequency renormalization. This constitutes
another dynamical consequence of the USC regime.
