Time-resolved two-dimensional photon-echo (2D PE) spectra of linear J-aggregates containing four molecules per unit cell a model system for a concentrated water solution of the pseudo-isocyanine dye-is theoretically considered. Analysis of a single unit cell and the full-sized aggregate is consistently carried out. Spectral features of a single unit cell are sorted out by assigning them to specific double-sided Feynman diagrams. Two different approaches of disorder are employed, the resulting differences in the spectra are discussed, and the conditions for their utilization are described. Special attention is paid to quantum coherence dynamics of a single unit cell and the full-sized J-aggregate. Possibilities of probing quantum coherences, as well as performing quantum control via two-color 2D PE spectroscopy, are discussed.