Before we talk planning, you can see from the diagram arrows that the tactical line 12.Nxd3 followed by c4 is available. A trade of c&b pawns for Whites e&d pawns = the center is Blacks; not to mention the monster on b7 is unopposed.
On to abstract thinking:
"I considered moving a knight to g4 with the idea of exchanging with
the dark-coloured bishop but such exchange would only give a pawn on
e3 which would challenge the control of the dark squares."
This line of thinking is extremely flawed!
Trading a knight for a bishop is rarely a bad idea. Doubling the opponents pawns is also rarely a bad idea.
In this particular case it is a good idea! Remember, doubled pawns have difficulty with mobility, and are therefore inherently weak. What do you think controls more dark squares, the Bishop on e3 or a pawn on e3?
Now, in general when the center is fluid, you need to be thinking about the center. "He who controls the spice controls the universe." and he who controls the center drives the battle.
So apart from the tactics available your planning should be around finishing development with an eye to conquering the center.
This position is so dynamic and full of tactics that it requires more concrete calculation than a long-term plan.
Edit due to comments -- more on fxe3 doubled pawns:
With resulting pawns on e3, e4, d3; yes the pawn on e3 controls f4 nicely, but look at the cluster -- it can't move!
The e4 pawn is attacked twice (so the d3 pawn is stuck) and it's advance is suicide. Therefore the e3 pawn isn't going anywhere either.
So now black can make long-term plans. Piling up behind the c-pawn to play c5-c4 can result in White getting double-isolated-pawns on the efile. Or setting up a battery of Bb6 and Qa7 hitting the weak e3 pawn... There are various ways for Black to attack due to Whites weakened structure. Now what can White do? Looks like just defend. His knights have no active squares and his remaining Bishop is thwarted. White is clearly worse here.