How does gravity bend light

Does gravity bend light and how long does it take for light to cross gravity in a black hole?

You are absolutely right: Einstein's theory is that the curvature of space is locally deformed. The essence of this is captured in the spacetime metric, a mathematical tool that tells us what space looks like and what is derived from it, what is meant by a “straight path” that photons take. In the absence of a gravitational source, a photon's path is what you intuitively know as a straight line. However, at some mass concentration (e.g. a black hole, as you say) that path is bent in such a way that the mass concentration acts as a lens. This is immediately apparent from this picture from the CFHTLenS survey:

Crucial to your question I think you need to remember that photons do not experience time and their speed is the same as c, the Speed ​​of Light. Photons are not unaffected by their movement through a gravitational field, mind you: this shows up as Gravitational redshift (for a time-varying potential) and not as a time delay (except maybe the slightly elongated path).

Also, the age of the universe is usually not measured entirely, as you say, but by estimating parameters, e.g. B. in the cosmic microwave background. The effect of the gravitational lens needs to be considered, but not in the way you think it is.

Also keep in mind that an extreme gravitational field like that of a black hole is relatively rare, and even if it delays the photon by 1000 years, it is still, in your view, a tiny fraction of the age we would be. shut down; The photon would have to hit a lot of such black holes for this "effect" (which does not occur) to have a major impact.

In general, you seem to have some (interstellar induced?) Misunderstandings about the universe, but I guess I can't address that here.