Elements in the timeline are organized in Groups. The groups are stacked in the same order things are rendered.
For a shape layer the first group is Contents. The twirly (>) has been turned down revealing the next element in the group named Shape 1 by default. There are more elements in the Shape 1 group that can be revealed. and they can be animated. The little circles in the Shape 1 row indicate that keyframes have been set at those times for the properties you can't see. Expand the group and you will see the animated properties. The > switch is a very useful tool for cleaning up and organizing your work in the timeline. When the properties are hidden they are protected. That is why you cannot delete the keyframes.
A faster way to see all keyframes on a layer is to select the layer and press the 'u' key. That will open all of the groups.
Understanding the rendering order is important to your workflow. In the shape layer the first thing that happens is that there is some kind of path of shape in the Shape 1 group that can be animated. That shape can be changed before the position of the layer is changed. If you were to add a Mask the Mask would be below the shape and above the position property. This means you could animate the Transform Shape 1 position and the shape would move but the mask would not. If you were to add effects to the layer they would render after the mask.
For more information on how the timeline panel works please check the User Guide. Spending an hour or so learning about the UI and the workflow will save you days of ineffectively poking around and waiting for answers from the forums.