Unsupported Ubuntus - is it safe to continue with them?

Well, better be concise:

  • Yes
  • No, there will be no updates.
    You will be able to install obsolete software from the EOL repositories, but nothing there will be updated and you will not receive help from this or other official help websites.
    Also, when the distro version becomes EOL you will have to follow a particular procedure to upgrade it to the next version (and not always works)
  • Yes (even before, so you have time to adapt to your new system)
  • No, a clean install will not be required. I upgraded 14.04>14.10>15.04>15.10 and I am not experiencing any problem (as it was in old times, where thing got broken pretty badly)

mate! Hope this helps you:

  • Yes, it means there will be no official support from canonical for 15.10. That is the reason why LTS is always recommended for people who need stability. You can still keep using 15.10 normally, tough.

  • Yes, you can patch and update your system from other sources and/or repositories, but I wouldn't recommend it. You can even install a newer kernell version, if you want, but in my opinion it is more practical to just install the newest LTS.

  • Yes. LTS is safer, stable and supported for a longer time (FYI I'm still using 14.04 and having a blast).

  • I think there will be an upgrade path. Check this page for more information: http://www.ubuntu.com/download/desktop/upgrade However, in my opinion it is better to do a clean install, since you will probably stay with 16.04 for some time. In my case, I think I'll wait until July of 2016 to upgrade to 16.04, for example. LTS is great because it gives you a lot of time to make your choice about upgrading.

Just a minor addition to two great answers: the most annoying thing for me about using an unsupported version is that a few months after the support window ends, apt-get stops working. The main apt repositories delete references to your version. Of course you can find archives and add them to your sources list and it starts working again, so this isn't a deal breaker. But it's one of those things that makes me feel like what I'm doing is probably a bad idea.

I actually recently downgraded some boxes from 14.10 to 14.04 because of this.