Yes to adjust the sensitivity of the circuit, use a trimmer in place of R2. Also a 1k or higer resistor is required in series with the trimmer to protect LDR from getting damaged due to over current when trimmer resistance is accidently set to zero.
NO the circuit won't drain much current in light because, the 100k resistor in series with LDR will drain around say (for 12V battery) 12V/100k=0.12mA which is very very small.
The circuit works like this:
1) When light is falling on LDR, its resistance is low and thus most of the current flows through it and almost no current flows through base of T2 and hence it is in OFF condition. So also T1 is in OFF condition.
2) Now in dark, LDR resistance increases and current now flows to low resistance path i.e. the base of T2 and hence it goes into saturation and also drives T1 in saturation thereby leading to current flow from emitter of T1 to its collector and thus energizing the flasher circuit.
Hope this much is sufficient. :roll: