How to run Windows 10 from an external hard drive? [duplicate]

Windows 10 (along with versions of 8 and 8.1) has a feature called Windows to Go. This feature is specific to the Enterprise and Education versions of the OS and allows them to be installed onto a USB drive as a portable Windows Environment.

However, you can do this without needing an Enterprise edition of Windows.

You'll need a few things to start:

• A 16GB or larger USB drive. Preferably USB 3.0. Microsoft sell certified 32GB drives as well.
• Installation media. Either a disc or .ISO will do here as you only need the .WIM file from the media.
• GImageX. This is a graphical frontend to the Windows Assessment and Deployment Kit tool called ImageX. It will let you install the .WIM file onto the USB drive.

Steps:

1. Mount your media, either .ISO or disc and navigate to the .WIM file is located, normally at X:\sources\install.wim where X is the drive letter of your mounted media.

2. Image the .WIM file onto your USB drive by using GImageX. This is fairly straight forward, just make sure you use the correct version (32-bit or 64-bit) of GImageX for your computer. Once GImageX is running, click the Apply tab,load up the source and point it at the drive letter of your USB drive.

This will take a while as this is actually install Windows onto the drive.

3. Mark the partition as Active using Disk Management.

4. Next we need to create Boot Entries for the drive. Run a command prompt as an Administrator and navigate to X:\windows\system32 and run bcdboot.exe X:\Windows /s X: /f ALL
   (X is your USB drive).

5. Done! Restart your computer and boot from your USB Drive.

Source and Images: http://www.howtogeek.com/196817/how-to-create-a-windows-to-go-usb-drive-without-the-enterprise-edition/

Is it possible to install and run Windows 10 on a portable external hard drive?

Yes. That is what "Windows To Go" is for. See my answer to another question Windows OS on external hard drive for much more information.

Windows To Go is a feature in Windows 8 Enterprise, Windows 10 Enterprise, and Windows 10 Education that allows them to boot and run from USB mass storage devices such as USB flash drives and external hard disk drives. It is a fully manageable corporate Windows environment.

It is intended to allow enterprise administrators to provide users with an imaged version of Windows that reflects the corporate desktop. Creation of Windows To Go drives is not officially supported by other Windows editions.

Source Windows To Go

There are various workaround for using Windows To Go with other versions of Windows, see 4 Tools To Create Windows To Go USB Of Windows 10 for example.

Is it considered legal to do so?

Yes. It must be as it is provided by Microsoft.