I’ll have a stab at answering the first part of the OPs question directly - even though I’m probably not qualified to. Mainly because it’s interesting to me and I’m interested to see if anyone has anything to add or correct.
Accuracy shouldn’t a problem, getting the probe to a point above the galaxy would be very straightforward - you’d have an enormous target area in which to point the probe so that would be easy.
The next problem would be the time it takes. Voyager was able to get a decent slingshot from a rare alignment of planets. Without that the probe would travel more slowly and we already know that Voyager is only just reaching the edge of the Sun’s influence. even with a fantastic sligshot it would take epoch-spanning years for the probe to reach the required distance (even with a super-duper wide angle lens).
Which brings us to life span. The probe would need to be built to last all those centuries. To withstand all the things that space throws at it. I’m not sure about this, but I’m guessing this would challenge us greatly. Maybe someone else knows more, but the engineers could set the path of the probe through a quiet part of space away from other stars to minimise radiation and so on.
Seeing as it’s going to be a long long journey, we need to power the probe. A piece of radioactive material might be harnessed to provide energy. Voyager turns radioactive thermal energy into electrical energy but I read that it will be forced to power down it’s last instrument no earlier than 2025. Perhaps it will exceed this by a decade or two, but that’s still not nearly long enough for our probe. Undoubtedly our technology will have improved and the half-life of some materials can be measured in hundreds of thousands or even millions and billions of years. Can we harness these enough to power our camera and communications? I don’t know, perhaps someone else can enlighten us.
And so… communications. Obviously the probe will be so distant at this point that any idea of two-way communication would be utterly ridiculous. So the probe will shout it’s information back to us and hope we can hear. Or, in fact see. Because I don’t think radio communication will cut it. This probe, I think, will need laser light communication. Which isn’t perfected yet. Although it’s surely not an insurmountable objective. And the probe would have to know where to point it’s laser. We might need to map the galaxy to a fine level of accuracy to allow the probe to look around and orientate itself. (Which would make taking the photo redundant, but hey we’re just trying to work out of we can do this right?) More power required. And the mechanisms to manoeuvre the craft and to remove the lens cap, to actuate the camera shutter or anything else would need to have lasted through all this time. In space.
That’s the probe. On a more practical level we’d have to ensure that the probe does not get forgotten. That we remember to look. The probe might contain a timer so we would be able to calculate the exact time we need to start looking for it. The sort of timelengths we are talking about are longer than the life expectancy of almost all of our storage technology. Instructions to look, how to decode the code the probe sends, and other technicalities might have to be passed down through the generations.
Finally, we would probably be able to invent better and better space craft which would be able to overtake our ancient probe. By the time the probe gets to it’s destination it might find a human colony of space archeologists, eagerly waiting for it’s arrival.
Without doubt I’ve failed to consider a very long list of requirements. I’m not a space engineer! BUt it was a fun to have a think about it…