Its a strange problem (or set of).
I personally tested it on Firefox/Opera and have issues with PM when running the entire board in secure mode. A member on the board has forced logout issues if we enable SSL Logins. But If you disable board wise SSL, but force it using HTTPS Anywhere (allow only secure connections) it works fine, apart from moaning about logins and posts being sent over an insecure connection, also even when the whole board is secured, it still moans because images arent being encrypted. For now we've decided to run it insecure until we are upgraded to the current version.
To be fair I suspect the issues lie in DNS, whoever set it up made a complete mess of it, lots of pointless entries, its on the todo list. Followed by a complete code audit. But until we have a fully upgraded board I don't see any point in doing any of that. Also the letsencrypt cert isn't ideal.
Thanks for your help anyway, it gives me something to play with.