With Minecraft Windows 10 Edition, do I get a Mojang Account? Power of desktop Minecraft?

You get a free Minecraft for Windows 10 account if you already have a regular Minecraft account. You just have to go to the website and enter your credentials and then it will activate it for Windows 10.

You will not get an old account to play the old Minecraft however. You will have to buy the new one for $10, but the old one will cost another $20 or so.

If you have a PC account you will receive a free copy of Win10 Version. You need to login to your Mojang account (not Minecraft account) and you will find a button marked 'redeem' Windows 10 version. If you buy it from the Windows store you do not (that I'm aware of) get a PC account. This is keeping with other Pocket Editions of the game.

To address your question about worlds. It does not appear that the world data is compatible. Win10 edition stores data using MSAccessDB where as PC version uses NBT data files.

It may be possible to convert in the future, but I couldn't find any such tool at this time. However, you should be able to transfer worlds between other MC Win10 versions (for example, I should be able to send you my Win10 world saves and they should, in theory, work just fine so long as you also use Win10 version)

Also, modding is not possible yet. Win10 version was a complete rewrite using C++ instead of Java. As such, they haven't included any mechanism to mod the game and typical techniques used with other versions won't work.

Mojang has stated they intend to make the game moddable in the future, however they haven't given a concrete timeline for this.

If you wish to have the ability to easily (relatively speaking) move worlds between users and play modded Minecraft you are better off acquiring a regular Minecraft account which will allow you to play Modded Minecraft as well normal Minecraft, and will also grant you a free copy of the MC for Win10.