In a way... you can
There is a program called Bluestacks App Player.
Playing minecraft on it is a bit dodgy though as it is an android emulator not a MineCraft PE conversion for PC use. MineCraft PE doesn't support physical keyboard yet, so all is on screen controls.
As you usually control minecraft on a phone with 2 hands (1 for movement controls and 1 for viewing around) on a computer you will have only 1. Your mouse. You can't rotate your view and move around at the same time, but technically you are running minecraft PE on a computer.
It is possible to play, but don't expect as good of an experience as on regular MineCraft nor MineCraft PE.
With some tweaks you are even able to create a lan session
Someone could try it on touch screen computers using windows 8. It may be a full MineCraft PE experience possibly. I don't have a touch computer though.
In the minecraft pocket edition you cant get seed because in the computer version you get seeds from tall grass and there is no tall grass in the minecraft pocket edition
You Can't get minecraft for free on pocket edition. I think it costs $7.99 for pocket edition, and $29.99 if you want it on the computer.
Pocket edition has later updates, but honestly get a computer, and get the game.
On a mac, if you have snow leopard or above, the App Store has Minecraft Pocket Edition (you need to pay for it). As for Windows, I'm not sure.
Yes there is signs in Minecraft Pocket edition
you cant have a minecraft pocket edition username
No, they are no enderman in Pocket Edition of Minecraft 0.8.1
When would Minecraft Pocket Edition 12.1 going to be out
Yes, there are villages in the updated Minecraft Pocket Edition.
As of Pocket Edition 0.3.0, cows have been part of Minecraft Pocket Edition. If you have that version or above, then there should be cows.
Minecraft Pocket Edition costs $6.99 in the Google Playstore or the Appstore.
You can not get minecarts on minecraft pocket edition. Also, minecarts are not planned for the next update.