Debian – can packages marked Debian/Ubuntu be installed in Linux Mint as well

Debian and Ubuntu are pretty good at upgrades, as long as you don't do anything to make them fail like tweak things in /usr. If you install a lot of third-party packages, they might have dependencies that complicate upgrades, so it can help to remove them before upgrading (if you “remove” and don't “purge”, your customizations in /etc will remain in place) and reinstall them afterwards.

Debian and Ubuntu use the same package format, and they often use the same package names, so it's sometimes possible to use a package intended for one system on the other. But don't count on it always working, as the dependencies aren't always in sync. You'll have a little better luck trying to recompile the packages from source. Better, if you use a lot of PPAs, use Ubuntu.

Debian's rolling release is called testing, or unstable if you don't mind broken dependencies.

Your questions are some what kind of complex so I don't think I can answer them all correctly. If someone read this post and see anything incorrect, please tell me to fix it. And also remind that I can only answer Debian - Ubuntu repo relationship, since I can't catch up Mint development goal and way.

1. Despite the fact that Ubuntu is based on Debian, it only picks the packages that it wants (89% as of 2010) then modifies them (Ubuntu regular stable releases draw from Debian unstable branch "Sid", while Ubuntu LTS releases draw from Debian testing branch, which draws from Sid). So depends on the goal, some Debian packages may be or may not be in Ubuntu. For now, 2015, Ubuntu and Debian are no longer compatible to use each other's repo.

2. No, you are not missing nothing. But also keep in mind that packages number can't say nothing due to packaging method, if you want real comparison, look for source packages number.

3. No exactly. As I mentioned, Ubuntu takes most of its repo from Debian Sid (or unstable, but I prefer the previous name) what is fairly up-to-date. Those softwares get tested, managed for a few (6, I think) months before get released in the schedule of twice a year. In Debian, softwares after got into Sid go to testing (after 10 days if no one can find more bugs). They might not ever go to Debian stable (what would be released) if they don't get to the right time, but if they get to testing in frozen time, they will get tested for another 7 months.

4. That's right, don't never try to do it unless you want to f*k your own system up. Mint is based on Ubuntu and the later 'un is based on Debian, but doesn't means they share the same dependencies. However, there is sth shared along Ubuntu and its derivatives: the ppa.

5. Well, yea, if saying sth like 90-95% then yes.

6. Like Drav Sloan said in his comment, they are not same distros. E.g. wit Debian , you can archive nearly perfect stability, but not in Ubuntu or you can't have attractive installer in Debian.

Debian's unstable branch is and will always be named "Sid", while the other branches (testing, stable, oldstable) are getting a unique codename for each release (Stretch (Debian 9, currently in testing), Jessie (Debian 8, currently stable), Wheezy (Debian 7, currently oldstable), Squeeze...). See this link for more and updated information.