First ting first, you cannot do double minification. You have to disable minification on w3tc or even on your theme options, if you have it.
Double minification breaks things, besides you are making your server repeat itself, thus slowing it down.
As for merging header and footer files, it doesn’t work the way you think it works.
You can move scripts to the footer, but there is no way to automatically move them from the footer to the header without breaking things. Nevertheless, moving your jQuery and possibly some other libraries such as galleries, etc, would break your site.
The order of execution matters, so if a developer enqueued their files on the header and others choose to enqueue them in the footer, there is probably a reason for that.
FVM doesn’t touch the order of scripts, it only merges and minifies whatever is in the header or whatever it’s on the footer separately.
If you hire a developer however, they can check if your scripts can be moved to the header or to the footer. It’s usually more compatible to move them to the header, but then they will probably need to edit some plugins code, which is not recommended if you want to keep doing updates.
That being said, you can try a plugin to move all your scripts to the footer, such as the one below:
https://www.ads-software.com/plugins/scripts-to-footerphp/
But be advised that some stuff may break and you may have “undefined” errors on the console log. Look into google chrome developer tools console, for information on that.
If your scripts are all in the footer, and if they are on the same domain, FVM will only use one file.
Also try the option to defer for pagespeed, and read our faqs.
https://www.ads-software.com/plugins/fast-velocity-minify/faq/