@bigphil :-
O-kay. First, I just want to clarify something....
That looks like a big, long scary list of things that aren't right. However, you can ignore it..!
Current Skype is an Electron-based application....all right? The Electron platform is built around a very stripped-back version of the Chromium browser. Chromium is the "daddy" of Chrome, Iron, Opera, Vivaldi, even M$ Edge nowadays; every single one of them is based around Chromium's code-base; thus, they all inherit its "quirks".
One of the 'quirks' of Chromium is that if you run it from the terminal, even if it fires-up & runs perfectly, a quick glance at the terminal shows a never-ending litany of complaints, and 'moaning' & 'whinging' about this, that or the other not being to the browser's liking. Yeah, I know; if there's that many things wrong with it, then how come it's running at all?
The devs at the Chromium Project wrote it to run this way for ONE simple reason; effectively, it gives a "live", real-time, ongoing debug session ALL THE TIME the browser is active. This helps to make it very easy for all their beta & dev version 'testers' to report issues, and ensures that problems in Chrome/Chromium et al tend to get fixed very promptly indeed.
And because Electron is based on Chromium, any Electron app, if launched via the terminal, will display that same, never-ending list of complaints; a 'noisy' terminal is perfectly normal for these browsers and associated apps, 'cos that's how they were built to work.....
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I take it you ARE aware that Skype needs to run-as-spot, yes..? The .deb package is written for mainstream distros, which expect that you're running from a dedicated /home directory as a "normal user". Of course, this isn't how Pup runs, is it?
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As to why it's crashing when you've initiated a call, hmm..... The only clue I can spot is that block of stuff about ALSA. Skype is written to expect PulseAudio to be on the system, and, with rare exceptions from Puppians who've built Puppies with it built-in, it's not a 'standard' component of Puppy. Normally, Pups are ALSA-only, all the way, so, to get round this, we usually install the 'apulse' libs from OscarTalks; these 'fool' apps into thinking that Pup's ALSA is actually PulseAudio, where in reality it's not. All it does is to translate PulseAudio system calls into ALSA system calls that Puppy can work with.
I would suggest, therefore, that you install them on the system, and then try again. You can find the newest version of 'apulse' here:-
http://smokey01.com/OscarTalks/apulse-0.1.13-x86_64.pet
See if that helps. Let us know how you get on, please..!
Mike.