Are black holes broken or incomplete worm holes?

Would a white hole have an event horizon?

White holes are unlikely to exist, but they are possible because solutions to Einstein's equations for general relativity (GR) allow it. There has been a lot of speculation and science fiction about them, but the causal aspects are pretty well described in Penrose charts, as shown in the Crowells posts.

Whether or not you define these white hole singularities as naked, it is clear that the white hole may have energy or information for the future. Doesn't mean a white hole exists, just that GR allows it. It may or may not be possible to have a shape.

There was more talk about white holes in connection with a so-called Einstein-Rosen bridge. It is a solution from GR that can be constructed mathematically and has a black hole on one side and a white hole on the other connected by the bridge. They have never been seen or discovered, so it is mostly speculation, but theory allows them under certain conditions.

See Penrose diagrams at https://en.m.wikipedia.org/wiki/Penrose_diagram, where you can see both black and white holes and wormholes

See wormholes at https://en.m.wikipedia.org/wiki/Wormhole#Schwarzschild_wormholes

The thing about wormhole solutions is that it was shown early on that the bridge between white and black holes (or most of them, but with the bridge instead of singularities) is not stable and collapses faster than light can cross it. This was shown by Wheeler, but it was later shown that if the bridge is allowed to contain "exotic" matter (essentially negative energy matter never observed), the bridge can be stable long enough to allow energy and information to come out of the black Hole can come region into the region of the White Hole and escape through its past horizon into a spacetime (sometimes also referred to as the universe, but that does not mean that the two outer regions cannot be connected to each other in any other way).

So the questions:

1) Can a white hole have an event horizon? Sure yes, it allows travel in one direction, from within the White Hole to the outside. Wormholes may allow a path from an almost black hole to another spacetime through an almost white hole. 2) Could it spit out random objects? For white holes, everything that emerges from the singularity of the past is spat out and there is no way of predicting what it is. For wormholes, it will be some form of what goes into the side of the black hole. The causality does not seem to be violated, there are no singularities.
3) Can this cause causal behavior? White holes might, but wormholes appear to be causal. 4) Doesn't the pure white hole violate causality, so that it propagates through future space-time and is therefore not "safe", as it is assumed that naked singularities do not exist? Seems so.

The unanswered questions or problems mean that classical GR or even quantum fields in a GR background are an incomplete theory and we need quantum gravity to get to what is in a black hole and what exists in the cases which describes GR as singularities.