Uhhh ... you probably shouldn't share that check link to your server here. But .... grade A looks good. And the section on mobile devices looks ok also.
But ... network comes before application (moodle in this case).
Students having problems:
How do they connect to the internet? A. via wireless to local lan which means their access to your moodle is via that provider. B. via wireless not connected to local lan but through the devices carrier.
If those students have a computer and are at home, can they connect? With a computer at home, they could install and use networking tools, like ping/traceroute, to see routes. They could also use Firefox and turn on it's networking tools to see show their access is fairing.
Access to a site is just not Device -> Site ... there are other routers/switches, etc. in between - in network terms 'hops'. Normally. if the number of hops is over 30 ... issues. Packets never return to the device requesting access/interaction.
Also, that error 'connection is not private' .. would also show if there were internal links in the moodle on the front page ... like for an image .. that was recorded in DB as http:// and not https://. So did your moodle recently change from http:// to https://?
So ... bottom line, this sounds like a connectivity issue for some users. Pick a tech savy student that has a computer and who could do things like FireFox, ping, traceroute kinds of things.
Sorry ... no simple answer!