Possible Duplicate:
How can I download an APK file from the Android Market?
I want to download APKs from the Android Market and sideload them to my Kindle Fire. I'm able to run APKs using ES File Explorer but not able to download them :(
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Sign up to join this communityPossible Duplicate:
How can I download an APK file from the Android Market?
I want to download APKs from the Android Market and sideload them to my Kindle Fire. I'm able to run APKs using ES File Explorer but not able to download them :(
The title of your question and it's body are really not very related to one another, but I think the title is actually something that's worth covering since I haven't really seen it come up here before (in a general sense).
Per the title of your question: You can't register a device on the Market from the web interface alone. Devices appear once the Market application has been configured on the device itself, at which point you can install applications via the web interface or from the device directly. The Market's website basically uses C2DM ("push") to install the app to the device over the air, it does not download the .apk to your computer.
So, per the body of your question: You cannot download .apk files from the Market website to sideload them - even with a registered device - so ES File Explorer is not going to help you with that. This has also been previously asked here: How can I download an APK file from the Play Store?
Your Kindle Fire will appear in your account (it most certainly does on mine, anyway) if you install the Market on it and log into your account from the device. There is a question regarding how to do this already: How can I get the Android Market installed on my Kindle Fire? Note that you must be rooted to do this.
The only way to add an Android device to Android Market is to install Google's core applications on it (including Market.) Unfortunately, Kindle Fire does not ship with "Google experience" apps, and there is no "official" way to install them. You must root the Kindle Fire first (voids your warranty,) and then install the Market's APK with supporting apps.
See this thread on XDA-Developers forum for an easy script. It's dated 1/9/2012, so be aware that it could be outdated if there has been an OS Upgrade for Kindle Fire recently. Browse other threads on the Kindle Fire Development section for other alternatives.