Can I really see what is on the opposite side of a black hole? This question is only about objects outside the event horizon. Both the observer and the object are just outside the event horizon.
I have read this question:

An observer can see the back side of the neutron star to some extent and can actually see the whole of the neutron star surface if the radius is below 1.76 times the Schwarzschild radius for its mass, $r_s = 2GM/c^2$. See https://physics.stackexchange.com/a/350814/43351 for details and some attempts to visualise this. e.g.



A neutron star with a radius less than $1.5r_s$ would distort a background star field in a similar way to a black hole, including the photon ring at an apparent radius of $2.7r_s$ caused by unstable circular photon orbits at $1.5r_s$.

Neutron star accurate visualization
Now based on this answer, the neutron star can bend light similar way to a black hole in certain cases, and using visible light, the whole surface might be visible, which means we can get information from the other (opposite) side of the object via visible light. Now visible light is just EM waves, like radio signals, and my question is about whether we can similarly receive visible light from someone on the opposite side of the black hole (because as the answer explains, the path of these EM waves are so bent, that they actually can go around the object).
Question:

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*Can I really see what is on the opposite side of a black hole?

 A: Yes.
You may have seen the visualization of a black hole in the film Interstellar. The following figure comes from Figure 13 of a companion paper (Ref. 1 -- note the author list includes Nobel Prize winner Kip Thorne). In it, you can see a disk in the upper left corner viewed at an angle. The same disk is viewed from the same angle in the center of the figure, but now there is a black hole inside the disk. As you can see, the black hole lenses the disk so you can see the part of the disk that you would normally think was "blocked" by the black hole.
One thing to note is that the image will depend on the spin of the black hole; in Interstellar, they chose a very large spin $a=0.99$ (in dimensionless units where $a=1$ is an extremal black hole with the largest possible spin), because you get more striking effects with large spin. Another thing to note is that there will be redshift effects that distort the colors; this is not accounted for in the image.


Reference
Ref. 1 James, von Tunzelmann, Franklin, Thorne.  Classical and Quantum Gravity 32 (2015) 065001. https://iopscience.iop.org/article/10.1088/0264-9381/32/6/065001. https://arxiv.org/abs/1502.03808
A: 
Árpád Szendrei asked: "Can I really see what is on the opposite side of a black hole?"

Yes. Let's take this 360°x180° full panorama:

Now we zoom in one direction:

and place a black hole in front of the observer:

Now we turn around by 180°:

and move the black hole into our new line of sight:

Here we look up 45° into the clouds:

and move the black hole into our view again:

As you can see we would see what's behind of us lensed around the black hole's shadow, but it would be strongly distorted.
The zoomed in images have a FOV of 103°x61°, the black hole has a spin of a=M. We only consider the black hole's gravitational lensing, not its destructive effects on the enviroment.
There's also a video here with the image used above, but the resolution is rather low. This video has a different background image, but higher resolution.
Since you tagged your question with "electromagnetism" as well you can also look at charged black holes here. You also tagged "quantum-mechanics", but this tag doesn't belong here in my opinion since the gravitational lensing is a GR, not a QM effect.
A: There is this new video showing the effect on Messier 87 black hole.
