How to view my project elements while working in a composition?
Short answer: yes.

Say you have a subcomp which you want to work on and you want to see how this affects the composition in which it is nested. This is easily done; you just need to open up a new viewer. You can have as many viewers open as you like (until your graphics card catches fire), this will let you see any number of linked compositions at once.

To do it from the menu go to View>New Viewer or hit Ctrl/CmdaltshiftN or right-click in your comp window and choose New>Viewer from the contextual menu. 

By default (?) this viewer will show the current composition (this is useful when working in 3D because you can set it to a different perspective), and it will switch when you change comps, so we have to lock it. That's what that little padlock icon is at the top of the comp window.


(I just noticed when taking this screen shot that the icon was already locked. Adobe may have changed the default behaviour of new viewers).

With this padlock locked the viewer will stay on whatever comp you set it to, so you can hop over to a child comp, make changes and see it update in the parent. You can drag your timeline to a new frame by dragging the tab, meaning you can see both timelines and compositions concurrently. Below is an example where you can see both a pre-comp and the composition it is used in, to allow for editing and live updating without switching tabs.