Most ground-based direct-imaging planet search campaigns use angular differential imaging that distorts the signal from extended sources, such as protoplanetary disks. In the case of the young system PDS 70, for which two planets were detected within the cavity of a protoplanetary disk, obtaining a reliable image of both planets and the disk is essential to understanding planet-disk interactions. Our goals are to reveal the true intensity of the planets and disk without self-subtraction effects for the first time, search for new giant planets beyond separations of 0.1$''$, and to study the morphology of the disk shaped by two massive planets. We present $YJHK$-band imaging, polarimetry, and spatially resolved spectroscopy of PDS 70 using near-simultaneous reference star differential imaging, also known as star-hopping. We created a radiative transfer model of the system to try to match the near-infrared imaging and polarimetric data within measurement errors. Sub-millimeter imaging data from ALMA were also modeled. Furthermore, we extracted the spectra of the planets and the disk and compared them. With strong constraints, we find that the disk is quite flared, with a scale height of sim 15<!PCT!> at the outer edge of the disk at sim 90 au, similar to some disks in the literature. The gap inside sim 50 au is estimated to have sim 1<!PCT!> of the dust density of the outer disk. The northeast outer disk arc seen in previous observations is likely the outer lip of the flared disk. Abundance ratios of sub-micron, micron, and grains estimated by the modeling indicate a shallow grain-size index greater than $-2.7$, instead of the canonical -3.5. There is both vertical and radial segregation of grains. Planet $c$ is well separated from the disk and has a spectrum similar to planet $b$, and it is clearly redder than the disk spectra. Planet $c$ is possibly associated with the sudden flaring of the disk starting at sim 50 au. We found no new planets in the system. If we assume DUSTY models and an age of 5 Myrs, this indicates no new planets more massive than 5 outside a 12 au separation.
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