I have upgraded debian 8 to 9 without any problems.So far I love it.Before upgrading I did not have any extra repositories enabled or ''installed(local or obsolete'' files.After upgrading I had some residual files which I cleaned.Since I did not have any obsolete files before upgrading(now I have some) is it safe to remove all of them?
Keep them. The only files safe to remove are auto removable files. There may be programs that depend on them to run.
Yup. That's the way it works in Debian/Ubuntu. The local/obsolete section usually lists programs installed through gdebi rather than through Synaptic package manager.