In this two-part paper, we investigate synthetic aperture radar (SAR) moving target imaging using planar antenna arrays. For a target moving over a three-dimensional terrain, its accurate localization requires the joint estimation of the motion-induced cross-range shift and the target height. In Part I of this two-part paper, starting from the planar array imaging geometry and the corresponding signal model, we show that these two quantities can be unified into a two-dimensional parameter vector and represented, after two-dimensional discrete Fourier transform (2D-DFT) processing across the planar array, through a natural vector remainder formulation. We first develop a general 2D-DFT matrix modulus framework and show that, in the two-dimensional setting, the associated 2D-DFT matrix modulus affects the propagation of vector remainder errors. Under a fixed array geometry and antenna number constraint, we derive an optimal construction of this matrix modulus and adopt it in the subsequent analysis. Under this construction, a single planar array provides only a folded estimate when the true parameter vector lies outside its unambiguous range. To resolve this ambiguity, we develop a multi-subarray framework in which multiple planar subarrays generate multiple vector remainders with different matrix moduli, and the desired parameter vector is recovered through the multidimensional Chinese remainder theorem (MD-CRT). To account for practical errors introduced by 2D-DFT quantization and additive noise, we further introduce an approximate 2D-DFT peak model for non-integer frequency vectors, incorporate robust MD-CRT, and establish sufficient conditions together with explicit reconstruction error bounds for both noiseless and noisy settings. Numerical results verify that the proposed multi-subarray framework enlarges the unambiguous range compared with a single planar array.