PS: I've looked through the FAQ and these questions don't seem to be covered. The FAQ appears to have been written for a much earlier version.
Aah, finally somebody that reads the FAQ
The FAQ is mostly about forum features though, not the game itself.
Let's see the symmetry feature first. When you place a part on the building grid, this allows you to automatically place the same part on the opposite side.
This is a fuel tank placed without symmetry:
And this is an engine placed with symmetry:
The game automatically placed an engine on the other side. This is useful to build boosters for example.
The rest of the buttons are about staging. Staging is a feature that allows you to pre-program your actions in flight. Let's take that rocket for example:
At lift-off, you'll click on the engine to turn it on. Then when you'll run out of fuel you'll click the separator to discard the first stage, then the second stage engine to turn it on and so on. Staging allows you to define these steps. First click on the "staging" button:
A new "+" button appears:
Click it to define a new step:
Then click on the Hawk engine to add it to your step:
Then add more steps and define your future actions like this:
You can also define several actions per step, it's useful to separate 2 boosters in a single move.
Then, in flight, just press on this button to trigger the actions you defined: