Is it possible for us to see our own galaxy from different perspective, as path of light emitted from our galaxy is curved by any possible ways and travelled back to our eyes even if it take much time?
I think the answer is 'yes, in theory, but no in practice'.
First of all, bear in mind that a black hole can deflect light through an arbitrarily large angle: if you've seen the images of the black hole in Interstallar then it has these strange patterns around it which are because light can circle it many times before escaping. (Formally, this is pretty much an argument from continuity, although I think it was a surprising effect!)
So, in particular, a black hole can deflect light back the way it came.
So all you need is a quiescent black hole (no accretion disk or other stuff to confuse the issue) and some light from any source will be deflected back the way it came. Well, let's assume there is at least one such black hole 'visible' to us, then at least some light from the galaxy is going to be deflected back to it.
So in that sense, some light from the galaxy will clearly be visible to us having been deflected around such an object.
- this will be a ludicrously tiny amount of light;
- I suspect strongly that there will be no useful image of the galaxy visible;
- knowing where to look would be extremely hard, since the BH needs to be quiescent and there would therefore not be any interesting EM (or, now, gravitational) radiation reaching us from it to tell us where it is.
So: yes in theory but no in practice.
Most of light emitted either reach other galaxies or escape to cosmological horizon. Our galaxies gravitational force is no enough to deflect it back.
Also, if it is deflected by some other black holes in a pattern, To get a complete veiw of galaxy we need light rays to simultaneously deflect back to us. Such possibility of a limited no. of such rays to to get to us is nill.
I know the context is bending of space by heavy bodies, but that is lensing effect and we know lenses do not reflect, however small their focal length is.
Even if it was possible to reflect/turn back good amount of light somehow, it would be next to impossible to see a meaningful image.
When moon reflects sunlight, we see moon, not the sun!
We can see sun's image in water, so, it would be only possible if there was a mirror type of object in universe and happen to be positioned just right for us. Which we know is not there.