Setting Up GMX Mail.

You're sure the gateway IP in the camera is set to the router/gateway IP?

Is your router providing/passing/allowing DNS to the cameras? When I set up firewall rules to keep the cameras from phoning home, a side effect was also blocking their DNS requests. Without being able to get DNS lookup, they could not resolve the domain name in the camera, e.g. smtp.gmail.com, to the necessary IP address so email sending failed.

Q1. All looks to be OK.
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Q2
I have set up no port forwarding, blocking etc. I have disabled upnp on the camera and router. Maybe this is the issue?
 
I have disabled upnp on the camera and router. Maybe this is the issue?
No, it's good to have disabled those anyway.
Assuming you have power-cycled the router, tested and it still would not allow an outgoing e-mail test then try this:

Since all the logical first steps have not born fruit, save or write down the router's configuration and do a hard reset. Log back in, upload that saved configuration file or put in those configurations you wrote down and try the email test again. This would be a last resort but I say this because 7 or 8 years ago I had a client's CenturyLink / Westell 327w DSL modem/wireless router that blocked outgoing e-mail and after all the normal, regular stuff failed, a reset/re-config solved it.
 
Not to hijack this post, but without having changed anything in my network (I got vlans, couple of gateways) my gmail connection from my NVR is broken. I looked in network logs left and right, and nothing gets blocked on the SMTP ports. So either google is "refusing" NVR spamming, or my internal code crashed. Not that I'm fully dependant of these emails as iDMSS gives me all required push notifications too.
 
As of 11 hours ago I've had no issues using Gmail through my NVR to send emails.

As of OP I'd temporarily set the NVR as dmz host just to see if it works or not. Of course I wouldn't leave that as a permanent fix. Just use it to see if you can send outbound or not.
 
As of 11 hours ago I've had no issues using Gmail through my NVR to send emails.

As of OP I'd temporarily set the NVR as dmz host just to see if it works or not. Of course I wouldn't leave that as a permanent fix. Just use it to see if you can send outbound or not.

I really don’t want to be putting my NAS in the DMZ. Maybe just the cam?
 
Can I make a back-to-basics networking suggestion:

Assuming it's an IP camera you're configuring for the GMX email, and assuming there may be some unknown network access rule getting in the way :

Temporarily unplug the camera from the POE switch, plug the PC in its place.
Set the PC IP address to match what the camera has, and also set the DNS targets to be the same as the camera.

At a Windows command prompt, verify name resolution as follows :
ping mail.gmx.com
and confirm that it resolves to an IP address and also gives a ping reply.
So far, so good if it does.

If name resolution doesn't work, try
nslookup mail.gmx.com

If that fails, try
nslookup mail.gmx.com 8.8.8.8
If that does work - there is a name resolution problem with your DNS target, presumably your router.
Re-try the email test in the camera with Google's 8.8.8.8 address for the DNS server.

If name resolution does work, try a ping to one of the GMX mail servers, for example :
ping 212.227.17.174
ping 212.227.17.184

If that does not work, check routing with this :
tracert 212.227.17.174
and wait for at least 10 hops to be tested.
If that fails, there may be an outbound block implemented in your firewall rules.

This should give some useful info about the network environment that the camera sees, although there could be some differences due to the PC being the test host.
 
Wow, that’s way above my basic networking knowledge but I’ll give it a try. Thanks.
 
I meant to add also - if the name resolution and outbound access via ping works OK, it would also be worth checking that the GMX mail server can be connected to via the chosen port.
You will likely have to add telnet capability to your Windows PC using -
Control Panel | Programs and Features | Turn Windows features on and off
and tick the Telnet box.

Then you can verify the access to mail.gmx.com port 587 using :
telnet mail.gmx.com 597 **edit** 587 - typo **
and check the reply from the server.

If that works OK - your networking is fine, and the problem must lie in the email configuration.