I've continued from here in reply to your More information post.
I'm not sure Firefox has changed in this respect as the "Application" tab has always been the same, as has download/save options in the General tab. But I won't contradict you as you have been used to things differently in the past.
However this is getting complicated because there are a range of different combinations that can be used here.
For example, email attachments should be different from normal web experience. But again, complications because I am guessing you manage your emails in the web browser, and not using email client software like Outlook, Thunderbird, Windows Live Mail, etc.
What you are doing with email attachments is right in my view. We always recommend saving emails to the hard disk so they can be scanned with the users anti-virus scanner before opening. When using email client software the anti-virus scanner, (if it is set up to scan emails, not all are), only takes a cursory look at the attachment. But when saved to the hard disk, the user can perform a manual full scan with the AV on the attachment. I assume that is the same when users manage emails in a web browser instead of using email client software, and in fact even more so. AV's do not scan web pages unless there is some specific AV Add-on included. This is because the AV scans the browser itself when it is first opened, then leaves it alone because it has done its job.
All that just to say, when you download a PDF file from an email, the file is then on your hard disk and not in the web browser. So when you open that file it should be opened by whichever application has been associated with .pdf files. I think that application is Foxit PDF Reader in your case. Note, I don't mean Firefox's Foxit Add-on, I mean the Foxit application itself which is installed on your system as a separate application.
So Firefox should not be involved in what you do with PDF files saved to hard disk from an email. The only way it might be involved is if Win 7's file association is set to use Firefox to open these PDF files. Whilst that is possible, it is not normal. PDF files on the hard drive would normally be opened by a stand-alone PDF reader application.
I have just tried this and get strange results. I downloaded any PDF file from a Google search to my hard drive. I scanned it, as normal, then clicked to open, (on my system I only need to click once, not twice). Foxit Reader opened to display the PDF file as expected. I then closed Foxit and right clicked this PDF file and selected "Open with". The Open With dialog opened and only Foxit displayed. I had to 'browse' to find another option and navigated to the Firefox folder and chose Firefox.exe. (I made absolutely sure that the option to "Always use this application to open this type of file was not ticked). Firefox then opened, (in fact a new tab because it was already open), and then Firefox offered me the choice of opening with Foxit, (the add-on), or Saving the file. That makes sense because Firefox treated this file as data from the network, usually the internet but in this case from source 127.0.0.1 which is the 'local computer'. I selected Open with and the PDF file then displayed in the Foxit application, not in the Foxit Add-on. How do I know that? I could move the Foxit window around independent of the browser window.
That confused me until I realised that I had not enabled the Foxit add-on in Firefox. When I enabled that, and tried again, the PDF opened in the new tab.
You can see how complicated this is, and I haven't even touched on the download options or the applications tab yet.
Now, in the Applications tab, when you highlight PDF files, (I have two entries for those), you get a choice of options from "Always ask", to "Save file", to "Use other...". The "Other" seems to offer which application to open with.
I assume that if you select "Use other..." and then Foxit, then any PDF file will open in the browser window, unless the Foxit add-on has been disabled, in which case the Foxit application will be opened to display the PDF.
But just to confuse this, the download options in the General tab may have an effect. If you select "Always ask" for downloads, but also select "Always ask" in Applications, does Firefox then ask twice? I don't know.
I'm not sure Mozilla, the makers of Firefox have thought these combinations through properly, but that is not only confined to Firefox as I suspect all browsers have this problem.
I'm not sure what else I can say except, 'sorry for the long and confusing post', and "Try all combinations" until you get it right for yourself.
I hope that helps.