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Your second point - I don't think the potential Planet Nine has anything to do with "problem with the orbits of some of the outer planets". It has been proposed as a solution to the orbits of some distant smaller Kuiper Belt objects. This in return doesn't really have anything to do with relativity, just basic orbital mechanics.

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I could have sworn there were problems with Pluto's orbit where it was faster/slower than it should have been, but it looks like I'm wrong.

>Specifically, this paper shows that, contrary to recent assertions in the literature, the current ephemeris for Pluto does not preclude the existence of the Pioneer effect. We show that the orbit of Pluto is currently not well enough characterized to make such an assertion.

https://arxiv.org/pdf/0905.0030.pdf

The Pioneer Effect has been explained as "anisotropic radiation pressure caused by the spacecraft's heat loss".

https://en.wikipedia.org/wiki/Pioneer_anomaly

That's an interesting case because they "solved" the problem by basically increasing the estimated uncertainty. See the dual sets of error bars in Fig 3: https://arxiv.org/abs/1204.2507

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