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We present spatially-resolved morphological properties of [CII] 158 μm, [OIII] 88 μm, dust, and rest-frame ultraviolet (UV) continuum emission for A1689-zD1, a strongly lensed, sub-L* galaxy at z=7.13, by utilizing deep Atacama Large Millimeter/submillimeter Array (ALMA) and Hubble Space Telescope (HST) observations. While the [OIII] line and UV continuum are compact, the [CII] line is extended up to a radius of r∼12 kpc. Using multi-band rest-frame far-infrared (FIR) continuum data ranging from 52-400 μm, we find an average dust temperature and emissivity index of Tdust=41+17−14 K and β=1.7+1.1−0.7, respectively, across the galaxy. We find slight differences in the dust continuum profiles at different wavelengths, which may indicate that the dust temperature decreases with distance. We map the star-formation rate (SFR) via IR and UV luminosities and determine a total SFR of 37±1 M⊙ yr−1 with an obscured fraction of 87%. While the [OIII] line is a good tracer of the SFR, the [CII] line shows deviation from the local L[CII]-SFR relations in the outskirts of the galaxy. Finally, we observe a clear difference in the line profile between [CII] and [OIII], with significant residuals (∼5σ) in the [OIII] line spectrum after subtracting a single Gaussian model. This suggests a possible origin of the extended [CII] structure from the cooling of hot ionized outflows. The extended [CII] and high-velocity [OIII] emission may both contribute in part to the high L[OIII]/L[CII] ratios recently reported in z>6 galaxies.