CC 2015 should enable you to navigate, change values, etc. without having to wait for the comp window to be calculated and rendered. In theory, you wouldn't need to use Caps Lock at all!
You're using the old (and much more buggy) version of CC 2015! You should seriously consider updating it. You want to be on 13.7.2 13.6 and 13.7 introduced some much-needed changes to the new preview architecture and fixed many bugs.
Upgraded to 13.7.2 and the layouts of the panels has totally changed. This is ridiculous. I'm rolling back to CC 2014. Adobe's updates are a joke. The lack of horizontal scroll bars across panel tabs was already frustrating enough, as were the new RAM preview settings.
You should give 13.7 a chance. (Remember, you can have CC 2014 installed alongside it, if you do get too frustrated and project files work between versions with no issues.)
The updates to 13.7 actually made the preview settings able to be very similar to the old RAM preview, but you get more customization to make it be the way YOU like to work, plus you get the improvements of the new architecture.
The PANELS! Those you should really give a chance. Try the all panels workspace. I found it much easier to work that way, especially on smaller screens.
I have verified this problem and filed a bug, thanks for reporting it.
However, this is not a new bug in After Effects CC 2015. This problem also exists in CC 2014.
If you use the Command key + left/right arrows to navigate between frames, the Composition panel preview will be updated even when the Caps Lock key is on.
However, if you use the PageUp and PageDown keys to navigate between frames, the Composition panel preview will not be updated when the Caps Lock key is on. This works in both After Effects CC 2015 and CC 2014.
(It's strange to me that After Effects is making a difference between which keyboard shortcut is being used for the same command. As noted, I've filed the bug.)
Regarding the panel layouts in After Effects CC 2015 (13.6 and later), you can continue to use the traditional tabbed panel interface. I suggest starting with the Standard workspace and customizing your layout from there.
Regarding scrolling tabbed panels, improvements for that will be in our upcoming release of After Effects. You will be able to scroll across tabs by panning them with the Hand tool (e.g., hold down the spacebar key, like you would in the Composition viewer), or hold down the Shift key and use the scroll wheel or scroll gestures.