Makoto

No, there is no way to do this natively at the moment, but I am planning to release a third-party plugin to do this soon as it's also an issue I deal with using GSuite.

You mean you want IPS to display the date members registered for your WordPress website, is that right?
You'll likely need some custom code to do this if so. The join date is just based on when accounts were added to IPS. The SSO plugin could certainly modify the join date to reflect the date they registered on WordPress, but you'd need a developer to modify your SSO plugin to do this.

How are you having emails sent on your server? Is this self-hosted or with Invision? If your mail server is very slow to respond/not responding at all, it can cause this to happen in some areas.

This was a bit difficult to track down but I think this may be the cause of your issue. Especially when you mention the user running a jailed version of Firefox, meaning they're likely very security conscious with their browser settings and may have this enabled.
https://discourse.mozilla.org/t/firefox-corrupts-any-image-i-paste-in-on-both-linux-and-windows/83459
The image you're pasting does somewhat appear like it's an entropy dump like in the above, so it's possible this is what they are experiencing. Have them take a look at this setting and try disabling it to see if that fixes the issue.
If it does, there's not really much that can be done to prevent it from happening in IPS itself outside of them keeping it disabled, or granting your site specifically permission to access that data.

This only happens in your phone? You are signing in to the same account both times?
I would say try disabling any third-party applications and plugins first just to rule that out, but this is an oddly specific issue.
Are you using the same wifi network on both devices too? Not really any plugin support for native Chrome on Android so that shouldn't be related either.

Awesome! Looks like this plugin might be the culprit,
If you have this installed and the issue goes away after disabling just this plugin, it's likely the culprit. In this case you'd need to contact the plugin author so they can fix any compatibility issues the plugin may be having.
 

Re-uploading the core files will only prompt you to update the applications you haven't already updated (in this case commerce)
It won't have any impact on the forums application, which has already been updated.
You could download the entire suite from the ACP and then upload upload the commerce/nexus application in the applications folder of that download, but I might suggest doing a full upload anyways just to make sure everything did get uploaded correctly when you did the initial upgrade.
IPS shouldn't let you upgrade if any of the files for a specific application weren't uploaded properly (so this means the forums, core software and other applications you updated should be fine), but it can't hurt to be extra sure.

Looks like this application may have some PHP compatability issues which are preventing your tasks from running properly,
Try disabling it and see if that resolves the issue. If it does, then you'll need to contact the author of this application and let them know of the errors.
 

In your AdminCP, under the System tab in the menu (the tab with the Cog icon that is active by default when logging in), click on Get Support, and then scroll down until you see an option to clear the system cache,

Cloudflare, for example, makes this very easy to do.
Just go Security, then WAF, and from there you can set up a rule to block an entire country code from accessing your server.

 
Just be sure you've carefully considered the implications, and you are certain you really want to do this.
(You can also block TOR exit relays via the country code firewall rule)

It's hard to say without looking at the traffic myself, trying to analyze what exactly they're doing specifically. Are they just trying to scrape your website, or trying to run malicious scripts? Things like that can give you a bit to go on.
In the latter case, enabling WAF rules could help, but you have to take a bit of care with those to ensure you don't cause false-positive triggers.
Blocking ASN's of entire web hosts where the malicious traffic is coming from is probably not a bad idea. Even if it seems like a hopeless endeavor, it may just take some time, monitoring, and persistence.
To some extent, though, you do have to account for this kind of traffic occurring and be able to scale with it as your website grows.

Here you go, my recommendations and advice;
http://community.invisionpower.com/topic/397051-pagespeed-web-server-module/