I'm using Ubuntu 11.10 but some repositories i have been using don't support new version of Ubuntu. So, is there any danger in using, say, Ubuntu 10.10 ("Koala") repository for Ubuntu 11.10? May I, also, use some Debian repository for my Ubuntu?
Package compatibility isn't determined by the choice repository, each package contains dependency declarations. As long as the packages are of reasonable quality, i.e. they declare the dependencies they're supposed to, you can continue to use that repository. If there's an incompatibility, you'll be told, because there'll be an unfulfilled dependency.
Using a repository that was intended for an older version of your distribution is very likely to work. If the repository's target version is very old, you may need to obtain older library versions from older Ubuntu releases.
Using a repository that was intended for another distribution is not so likely to work in general, because different distributions break down packages in different ways. In the specific case of Debian and Ubuntu, Ubuntu is a derivative of Debian and retains a lot of the package structure, so repositories intended for one usually work well on the other.