Peltier Module TEC1-12706 draws only 2.7A. Is it normal or my unit is defective?
There are a bunch of these devices available at very cheap prices.... not unexpectedly though many have either intermittent or broken connections to some of the elements.  When you see the prices vary from close $2 a piece through to $15 a piece it's hardly a surprise that defects and dropouts make it into the market. You will see devices quoted from QC of 50W through to close to 100W.

Sounds like you have some intermittent connections in your device. 

There are a bunch of datasheets too ...here's one.