Does gravity bend light, and how much time does it take for light to cross gravity of a Black Hole?
You are quite right: Einstein's theory says 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, derived from this, what is meant by 'a straight path', which photons take. If there is no source of gravitation present, the path of a photon will be what you know intuitively as a straight line. However, for some mass concentration (e.g. a black hole, as you say), this path will be bended such that the mass concentration acts as a lens. This is immediately clear from this image from the CFHTLenS survey:



Crucially to your question I think, you must remember that photons do not experience time and their speed is equal to $c$, the speed of light. Photons are not unaffected by their movement through a gravitational field, mind you: but this shows up as a gravitational redshift (for a time-varying potential), rather than a time delay (other than the slightly elongated path, perhaps). 

Besides that, the age of the Universe is typically not quite measured as you say, but rather through parameter estimation in e.g. the cosmic microwave background. The effect of gravitational lensing needs to be taken into account for that, but not in the way you presume. 

Also, remember that an extreme gravitational field such as that of a black hole is relatively rare, and even if it did delay the photon for a 1000 years that is still a tiny fraction of the age we would, according to your way of thinking, infer; the photon would have to encounter a LOT of such black holes for this 'effect' (which does not occur) to have a huge impact.

As a general point, you seem to have some (Interstellar-induced?) misconceptions about the universe, but I think that's not for me to address here.