Is the transferring of "consciousness" from one person to another person is possible if a brain transplantation is possible ?
Is it possible to pick memories from the brain by using EEG?
Since the two first questions are covered by the dupe question, let's answer the EEG part.
A quick google gives me this article :
It's important to remember that EEG can't actually read a person's thoughts. Instead, it connects neuronal patterns with actions or mental states. "If I move my right hand, and that creates a very clear signal that links to a computer command, that’s an entirely different beast than me simply wanting my character in the game to turn left and turn right"
Of course we understand want you want to do but it is quite risky especially in a real world situation (in a fiction work you can do anything). For example in S03E01 of Rick and Morty, Rick is trapped in a simulation where an entity wants it to remember a specific part of his life where he writes a crucial math equation. Rick tricks the entity by creating a false memory (writing another equation).
You can very easily manipulate memories on people, making them think something happened, especially with peer pressure ("hey I remember that too!").
In conclusion, in a real situation it is quite impossible since memories are not reliable. But in a fiction work you can handwave any futuristic/magical device that can isolate a fresh memory.