playing different animations at same time

Hello there, you can solve your problem by selecting multiple lyers in the timeline. After that select Pre compose for main menu and click on pre-composition in the timeline and play its layers in composition. In this way you can play different clips.

Create a new composition then drag all 3 of your other comps into the new comp. It is called nesting. 

For specifics, we need you to show us screenshots and give us a complete workflow description. It sounds like you are very new to After Effects.  Please, spend some time with the User Guide and explore the resources on the Welcome Screen and in the Windows/Workspaces/Learn menu. 

* The "Drag & Drop here..." area is buggy and should not be used to share images. Please use the toolbar or just drag your images to the reply field.