Some progress has been made today. Problems start to show now, which was expected. However we can at least see in which scenarios it goes wrong now.
Most of the time the movement and collision is correct. But especially in corners where there are three tiles that are being collided with, the collision is incorrect. I have no clue why it happens. As sometimes it also thinks it is moving to the right while colliding on the left. I just have to hook up the debugger and see why the code makes those wrong decisions.