I'm using BitTorrent for downloading whenever I don't use my laptop.
Can I have downloading from the Internet when my laptop is in Standby Mode or something to cutback electricity using ?
I'm Using Windows 7.
No, you can't. When the computer is in standby mode it is off, except for the memory being constantly refreshed (if you don't refresh the memory it clears).
If you want to perform network activity the computer must be on so that the CPU can execute application instructions. If you want to save power I suggest turning your monitor off or setting power-saving settings in your operating system (such as auto-monitor standby after a period of time).
Note that the application you suggested will probably also want to access a hard drive or other storage mechanism.
Very simply, no.
However, most p2p clients do include a setting which allows your computer to either be put into standby, hibernation or to be completely switched off once downloads have completed.
For the BitTorrent client, I believe you simply go to Options and then Auto Shutdown for this.
Ensuring your laptop screen is switched off (ensure you set 'Do nothing' for the option 'Choose what closing the lid does' from Power Settings in the Control Panel) and the wireless is disabled (if connecting via a LAN cable) will also help. Wireless is one of the largest draws of power on a laptop.
A solution would be to buy a NAS (Network Attached Storage) that supports BitTorrent.
For instance, QNAP makes such NASes. Apart from providing disk space to computers attached to the LAN, the QNAP NAS boxes have a lot of other features, including:
They use Linux and can also run PHP, MySQL, websites, ...
I bought the Qnap TS-210 and I'm very satisfied with it.