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First of all, it seems your picture about tf tree doesnt have amcl, so I'm not sure if the picture is related to the questions.

Next, following are my thoughts about your questions:

1. You are right. AMCL keeps transform between map and odom. Some node will keep transform between odom and base_link. This node could use difference ways to calculate the transform: motor encoder, laser odometry, imu, fusion of different sensors, etc.
2. Not always true. The reason is it depends on the rotational transform between odom and map. In your example, there is no information about the rotation, so we cant conclude easily. If the odom and map frame have same orientation (meaning no rotational transform between them), then you can conclude x=x1+x2, y=y1+y2.
3. base_link frame represents the robot body. It varies from different type of robots. For ground robot and UAV, it normally is the center of rotation of the robot.

First of all, it seems your picture about tf tree doesnt have amcl, so I'm not sure if the picture is related to the questions.

Next, following are my thoughts about your questions:

1. You are right. AMCL keeps transform between map and odom. Some node will keep transform between odom and base_link. This node could use difference ways to calculate the transform: motor encoder, laser odometry, imu, fusion of different sensors, etc.
2. Not always true. The reason is it depends on the rotational transform between odom and map. In your example, there is no information about the rotation, so we cant conclude easily. If the odom and map frame have same orientation (meaning no rotational transform between them), then you can conclude x=x1+x2, y=y1+y2.
3. base_link frame represents the robot body. It varies from different type of robots. For ground robot and UAV, it normally is the center of rotation of the robot. robots.