Is it possible to check from the EM waves(basically Light rays), if there are any extraterrestrial objects interference/passage during its travel from the Sun? I mean, can these EMs from the Sun be visually reproduced to pictures to see what has happened to these waves en route from the Sun?
Yes and no:
EM is already an important way of "checking": Sun spots are places where no EM is emitted, causing us to see them. If the moon passes between the Sun and Earth, we have an extraterrestrial body interacting with EM (blocking in this case), and we can have a picture of it (an eclipse).
However, this is only true for big bodies such has the moon. Smaller objects don't block the light, they diffract it, causing a diffraction pattern. The problem is that for long enough distances has the Earth-Sun distance, it becomes impossible to distinguish the patterns. The analogy is to imagine that you are looking at a bright light (e.g. lamp), and trying to define a tiny bit of dust on its bulb.
Other problems arise such has the atmosphere interaction, but the main limitation is diffraction.