Is it possible that there is an intelligent life form living exactly to the other side of the Milky Way from us, and we cannot detect anything about them as the galactic center blocks our view?
There is something known as Earth Similarity Index which lists few Earth like planets but nobody knows weather there is intelligent life or not.
There's also Kardashev Scale, its a method of measure civilization's energy consumption.
Type 1 civilization, we can detect them by orbital belt of satellites around a planet.
Type 2 civilization, we can detect them by Dyson Sphere/Swarm.
Nothing found yet!
Sure, why not. Milky way is a very big galaxy and there may be billions of planets around billions of stars like our sun. Tracking one particular evolved planet out of billions is itself a difficult task let alone search for life on those distant worlds on the other side of milky way is quite impossible .
It is not necessary to go all that distance yet. There may be many planets like our earth on the solar system side of the galaxy itself for all we know. It might take ages to detect planets that harbor intelligent life. It is a matter of searching the space in the hope of getting a lock on to the specific area of the origins of signals and it takes time and patience.
For all we know, there is an intelligent life in Proxima Centauri b( which is one of the closest exoplanets and is in habitable zone). Honestly, our lack of knowledge of Alien life is profound. But that doesn't mean that they cannot exist. You see, in our own earth there are many animals that have adapted to living in conditions that would kill others. So there is a chance that even in conditions harsher than for humans, you might find alien life. But it's all speculations, till we find actual proof. And yeah, there might be 100s of sentient civilizations in Milky Way. We just don't know for sure yet.
The problem is not the galactic centre. The problem is that we have only been broadcasting for about 100 years and only listening for maybe 60.
That means our SETI can only pick up signs of transmissions 60 light years away. As you know, the Milky Way is 100,000 light years across. We have not gotten ANYWHERE close to the galactic centre yet and will not for many thousands of years