No. To keep the process simple for both us and you (and to insure you have a large amount of flexibility in the use of our template tags) we do not resize your media files. This could be an option on future release.
Due to the way WordPress handles post ID's on an archive page, or the blog homepage, the first post is what will determine what dynamic media is pulled. You can overwrite the image for the homepage on the plugin's Settings page. We plan to add override support for the other archive pages on a future release.
Absolutely not. You are limited only by your imagination (and theme editing abilities) on how/where you want to drop the dynamic media tag in your theme.
Sure, just upload your media to /wp-content/header-images/.




