Well, if you can give me link and panel login, I can check for certain.
Basically, if you can save anything without "http" in the text, but then it doesn't work with "http", it means it's a firewall. Why else would it fail randomly like that? It's just text.
They can't help me because there is no restriction on my webspace.
What does that mean? Does it mean they are not using a firewall or mod_security? I'm gonna be direct with you: Based on what you told me, I am pretty sure I will identify (with screenshots) that this is a firewall/security issue on your server. Why else would it block ONLY when "http" text is in the content? This is a typical example of a firewall rule used wrong.
When I have screenshots with network output to show this, you will have to contact your host about it. If they are a professional host, they will help solve the issue.