Non-free repositories are useful because they allow you to install proprietary software which you might need or want. I've noticed that the non-free repositories don't include some of the proprietary software I'd like to run - i.e. Skype, Telegram, and Kodak Verite drivers. Why is it that software like that isn't in the non-free repositories?

You need to install e.g. Skype by downloading and installing it manually.
Then the package installs the repo.

Important notice: All Skype for Linux clients version 4.3 and older will be retired on July 1, 2017. To keep chatting, please install the latest version of Skype for Linux. said Skype.
v4.3 in repos. Are Deader than MySpace.

I have not tried the very latest version of Linux for Skype. But I believe Linux for Skype is still outdated and badly maintained.

The good news is that Skype comes in a web version: web.skype.com. Logging in with your Skype ID presents the contacts and everything you had before in the desktop client.

Skype for Web runs well in Chrome, but has problems in Firefox.

In Windows, you have to install a plugin in Chrome or Firefox (why???) which failed for me in both browsers. Only Edge doesn't need a plugin and works well. Where have I seen that MS policy before?

AFAIK in Linux Skype for Web still runs without plugin.

It works 95% of the time. My wife can call me from her Chrome OS. But I cannot be the one who initiates the call.

As alternative we use Google Hangouts. Google is also evil of course but it Just Works.

jlinkels

"skypeforlinux" is the new package name, for this platform anyway.

v5.4.0.1 is what I show.

The newest client also has an option to "Export chat history from Skype 4.3"
It's new as of 5x and it reads the old ~/.Skype/<Identity>/main.db file.

Previously I use Skyperious for this activity.
Desktop Sharing, is of course, now a missing feature.