Jennifer Morrow (part of the Firefox user experience design team) wrote a pretty detailed blog post about removing the Firefox status bar in 2010. As already mentioned, the aim was to remove the unnecessary "chrome" from the Firefox UI. I'd recommend you read the whole post. A short extract:
The goal is to find places where chrome can be minimized, both through
efficient redesign and pure removal where functionality just isn’t
providing enough benefit. This process led us to an obvious candidate
for chrome reduction: the status bar. In addition to taking up page
content, the status bar is the only part of Firefox’s permanent UI
located on the bottom of the browser. This placement leads to the
status bar being easily obscured, and sometimes requires resizing the
window to view. For an entire toolbar of UI, it seems this slacker may
not be pulling its weight in usefulness.
It is possible to re-introduce the status bar through an add-on.
As to the shortcuts, it looks like Ctrl+Shift+Y is still the default shortcut for Firefox in Linux to open the download manager, even though Chrome in Linux uses Ctrl+J (as you pointed out, the Windows shortcuts are identical: Ctrl+J). As you probably know, the default shortcuts can be customised to your liking.
I think it would be naive to think that the browser developers/designers don't compare their product with the competition. Jennifer makes reference to Chrome's UI design choices as early as Feb 2009 in her post "UI redundancies":
This is an observation more than a criticism, but have you ever
noticed how many redundancies occur in Firefox? Chrome’s tack has been
to eliminate some of these and scrap the interface down to the bare
minimum, which is probably going too far, but perhaps there are ways
to clean the UI in places without sacrificing functionality or
When it comes to tabs, the Mozilla team is doing lots of interesting research to determine how users use tabs. One example that may provide an answer to your tab question is found in how many new tabs users create each day:
Using Mozilla Test Pilot, we began to research how Firefox users use
New Tabs. What we learned is that each day, the average Firefox user
creates 11 New Tabs, loads 7 pages from a New Tab, and visits two
unique domains from a New Tab. The average New Tab loads two pages
before the user closes or leaves it.
Although the above extract comes from a post in 2012 on the redesign of the home and new tabs, I believe they had an intuition that people would be more likely to use tabs, than not use tabs (hence keeping the tab-bar visible at all times).
The add-on manager has many blog posts dedicated to its redesign. The rationale for making it a tab is briefly mentioned in a December 2010 post:
Instead of managing your add-ons in a small, separate window, the
add-ons manager now loads in a tab. This means it won’t be so small
and easily lost among other windows, and you can interact with it
identically to other tabs, including resizing and moving.
Lastly, you might find the following worthwhile as an answer to your question: Alex Faaborg (another one of Mozilla's designers, although he has since left the company) gave a talk at PARC in 2011 titled "Designing Firefox" (link to his blog, where you will find various download links to the video). It was presented during the transition from Firefox 3 to 4, where a lot of the UI changes started to take place. Here is a short introductory text by Steve Williams:
While much open source software suffers from poor design and
usability, Firefox shines. What makes the Mozilla community different?
With great branding, usability backed up by research but tempered by
realism, and a powerful extension architecture, the Firefox web
browser claims 400 million users. On the eve of the release of Firefox
4, Mozilla designer Alex Faaborg covers the unique challenge of
coordinating user experience design in an open source community,
important features of past versions, and the future of the Firefox
Overall I believe a lot of thought is put into the UI changes, and it is worth keeping an eye on the blogs of these UX teams.
Edit: I noticed that someone else asked a similar question about Firefox's last tab before here at UX.SE, so the answers to that post may be relevant as well.