I have a Wireless internet connection and a Lan Connection. I want to use both of them at a the same time using 2 different browsers. Is this possible ? *** let me know.

Why would you want to ?
Just use the fastest of the two, most likely the LAN connection.

Using one connection for torrent hence the bandwidth is low for other usages. So I have a wifi connection that I need to use for other online stuff.

Are both the Wifi and LAN on the same OUTGOING internet connection ?

Here's an idea, turn OFF the piracy enabling torrent client. It's a MAJOR bandwidth hog.