Case Type page blank
Seems like apache mod_security was the culprit. I deactivated it temporarilly and CiviCRM Case Types page works just fine. Now I need to find out exactly what rules are causing the issue.

EDIT: In my case I added the IDs for REQUEST-42-APPLICATION-ATTACK-SQLI to the ModSecurity whitelist and the issue disappeared. I realise this is probably not ideal - it would be better to write an exception rule just for civi queries, but that's beyond my current knowledge.

I think the CiviCRM dev or docs team needs to look into this as likely more people will have this type of server configuration by default.