It is known that the Forex daily volume is about $1.5 trillion.
Question:
Does this amount include leverage, or is it the 'real money' traded volume ?
If it includes leverage, what is the real traded amount ?

That is the real money traded, but perhaps you need to understand the
most forex transactions are "day trading" by financial institutions,
buying and selling individual contracts for many millions of dollars,
but at the end of the day, their "open position"  - whether they are
long or short in their home currency -  is very much smaller.

Does that help?

Dear Myoarin, 

Thanks for your comment. 
Do you have an idea of how much average "open position" total margin
volume is at the end of the day ??

Hi Michel,
The open position allowed by management varies depending on the size*
of the bank and management's risk attitude when setting the limit that
the dealers have to stay within, otherwise they need to get approval
for having exceeded the limit.
However, with global institutions and 24 hour trading around the
world, the open position in a bank's operation on one continent can
passed on  - say, from Europe to USA -  so that the NY office can
cover the open position in Europe.

*Size:  An open position (also for derivatives) is included in balance
sheet risk ratios that are set by local bank law and other directives.

CHeers, Myoarin