No, unfortunately not. MWI requires the “Mage.php” from your Magento store to be included using PHP, this means it needs to be on the same server as your WordPress Installation. On top of this, session data is store per server, so even if we could include the file, the sessions wouldn’t work.
You can however use MWI with subdomains. These are usually hosted on the same server, assuming both Magento and WordPress share the same main domain name.
Yes, you can. Simply purchase and activate the “Shortcodes & Widgets” add-on, and read the documentation for usage instructions.
It should work pretty well with most versions of Magento, but I’d definitely recommend 1.5+. If you have any issues with lower versions, just let me know.