Limits of electromagnetic source detection? What distance from the observer a lightbulb must have so you can't say the light was from this lightbulb?
Is it possible in astrophysics to detect a farest star or galaxy only measuring separate photons?
 A: photons have infinite range, but in traveling away from their source into 3-D space they get spread apart more and more, so here on earth our detectors would catch fewer and fewer of them, the farther away the source was.
At some point, there will be too few of them to trigger the detector- and the source then becomes invisible, unless you wait a very long time (weeks!) to collect enough photons to see their source. This is exactly what the Hubble space telescope did, in its deep space survey.
Note also that in interstellar space there are clouds of gas and dust which will dim the light passing through them, and then there will be no photons left to pass through the cloud and then catch on earth.
An individual photon carries no information about its source, except its wavelength, which tells us how hot the source was then the photon was emitted. to identify the far-away source requires us to catch a lot of its photons and measure their different wavelengths. This is called spectral analysis and allows us to figure out what the source was- a single star that is newly-born, a cloud of stars that are all very old, synchrotron radiation from an astrophysical jet, a gas cloud full of hot molecules, the active core of a distant galaxy, etc.
