We investigate chiral transfer and dissipative generation of even-parity Bell states in a two-qubit system with coherent two-photon driving and engineered two-photon loss. We find that adiabatic encirclement of a second-order exceptional point induces direction-dependent transfer between the Bell states |Φ⁺⟩ and |Φ⁻⟩, governed by a time-integrated low-loss branch-selection mechanism. We develop a hybrid-Liouvillian description with a control parameter q that interpolates between conditional no-jump dynamics and unconditional Lindblad evolution, and use it to assess how exceptional-point-induced chirality survives in the presence of quantum jumps. When the same parameter loop is initialized in the separable state |00⟩, it directly generates strong even-parity entanglement. Together, these results extend dissipative Bell-state control beyond the single-excitation manifold. They further demonstrate that exceptional-point-based protocols can unify chiral state transfer and entanglement generation within a single engineered two-photon platform.