Is a black hole a perfect sphere? I know all about how black holes form and why their gravity is so strong. However, is the gravity equally powerful in all directions? Will the event horizon appear as a perfect sphere?
You cannot see the event horizon. That being said:

A non-rotating black hole, free of external influences, has perfect spherical symmetry. All its properties are exactly the same in any direction, period. This is the Schwarzschild metric.

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

Even if it is electrically charged, if it's non-rotating, and free of external influences, it is still perfectly spherically symmetrical - this is the Reissner–Nordström metric.

https://en.wikipedia.org/wiki/Reissner%E2%80%93Nordstr%C3%B6m_metric

As soon as it begins rotating, the black hole is no longer in perfect spherical symmetry. It acquires an ergosphere, which is shaped like a flattened ball. This is the Kerr metric.

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



Significant external factors can distort the shape of the event horizon. Two black holes merging will go through a process where spherical symmetry is lost temporarily:

https://www.youtube.com/watch?v=JOQMvyLYmd4

Technically, anything near a BH would slightly distort the metric of spacetime, but in practice this would not be easily measurable unless the external factor is very large (another very massive object). So for most practical purposes, the metrics described above would apply.