can i download linux to ext hard drive,format laptop and install linux on it

Download an ISO, burn it to a CD/DVD/USB flash drive, boot off the flash drive, and install.
You can burn it to an external HDD if that is the only thing on the HDD. You can use LiLi to create bootable flash drives. Windows has a built in utility to burn CD/DVDs.

Sure you can replace the proprietary Operating system originally installed in your computer however before you do that you should make sure the OS you are planning on install is fully compatible with all the hardware in your machine.

In words you can tell us here what is the brand and model of your computer that will be a start. Perhaps somebody here has had previous experience with that same model
Running a live session will help to determine if all your hardware is compatible. While runnin the live session check that your wireless card and video (If any) works good.

As suggested above on the previous post you can download the ISO image file of a Linux Base Operating system and burn it to a CD or DVD and boot your computer from the CD or DVD.

Alternatively you can use that ISO to create a bootable flashdrive and boot your computer from that drive. You will need a software like unetbootin to accomplish that. If you are currently running windows download the windows version here is the link http://unetbootin.sourceforge.net/

Some of the Linux distributions that known for being user friendly are

Linux Mint --------------> http://linuxmint.com/
OpenSuSE ----------------> http://www.opensuse.org/en/
Ubuntu ------------------> http://www.ubuntu.com/

Let us know how it goes, and Good luck to you.