English

I plan to play someone who plays the English in every game as white. I would like to know the ins and outs of the opening, traps to look for and sound black counters.

1.c4 c5 - Symmetric English, leads to positional play. Black simply copies White's moves. Ultimately, one player or the other must take a risk and break the symmetry if they want to win, often with d4 or d5 but sometimes other ways. Sometimes neither player breaks the symmetry and a draw is agreed to.

1.c4 e5 -  This line leads to active, tactical play. Typically both sides bring out their knights (2.Nc3 Nf6 3.Nf3 Nc6... Four Knights variation) and then either 4.e3 or 4.g3 followed by 4...Bb4 and then the fireworks begin. Warning! If you attempt to attack before bringing out both your knights you are likely to fall into a trap unless you spend some time preparing  your variation.

This is a common one:

Here's an example of what I meant. It's an obvious fork, but I pick up wins from time to time when my opponents miss it.
 

Yup. White's pawn ends up on d5 in several lines.

In the game above white got a fianchetto underway. Is that pretty standard?

Also, I have heard that the aim for white in the English is to control the white squares in the centre (but not ocupy). Is that correct?

Both statements are often true but more often untrue. The English is extremely flexible. I may attack on the kingside, queenside, or center depending on where I believe I will have the most advantage. It's different from many openings where both sides have fairly concrete attacking plans early on. 

Sorry, I only understand about 35 opening positions. When I was starting out I memorized almost 500 before realizing how silly that was.

I like the Rubinstein variation as black, wherein I try to set up a maroczy bind.

It goes, 1.c4 c5 2. g3 Nf6 3. Bg2 d5 4. cxd5 Nxd5 5. Nc3 Nc7

with Nc6 and e5 to follow