Add button and Content dropdown are missing in After Effects

What are you trying to add? Select a layer and go to the Effects menu or the Effects and Presets panel to add an effect or preset. Choose the Pen tool (g) to add a mask.

Contents are only in Shape layers. Just start spinning down the properties of a shape layer that has something in it.

Shape layers and text layers are the only layers with Add buttons. You find the add button at the top of the properties stack when you spin down the properties in a Shape or Text layer. 

Your screenshots only show Solids. There are no Contents or Add options for shape layers, footage, or nested compositions (pre-comps).