1. No, simply no. It makes my eyes go funny.
2. No. Cute ways to make graphics spell out a company's name is a first-year student's approach. You can do better. It looks like a QR code FFS.
3. Interesting. But what does it have to do with browsers? Is Mozilla now making robots? Or a chat app?
4. Cute. Will not be cute in about 18 months.
5. No, and see point 2 as to why. It also does not render well at 32x32.
6. Makes my eyes bleed almost as much as #1. Also will not render well at low resolutions. FFS, why do I want to recall those horrid Apple drawing programs from the pre-iMac days?
7. What? Which part of that is the logo? Is Mozilla an origami company now? It's supposed to read Mozilla? See objection to #2.
The only one that has any relevant design sensibility (note the important "relevant" part ... the open elevator door logo is sheer idiocy, unless Mozilla has bought Otis Elevator and no-one's noticed) is the fourth Moz://a, but it will get tired quickly. Cute does not last.
Now, can anyone tell me what the Mozilla logo currently is? Not the Firefox logo. Not the Thunderbird logo, but the Mozilla Foundation's logo. Anyone? Anyone? So the logo does not matter one whit. (The logo, having looked at the mozilla.org web site appears to be a lower-case "mozilla" in an attractive sans-serif font; not a bad logo, kind of bland, but lacks the iconic symbology that is regrettably so popular right now.)