Just FYI... (I recently restored my phone and re-set up my email accounts), and...
I am -not- using the gmail app... I'm using Apple's built-in client. First...
- For my gmail account, it set its server "Gmail SMTP Server" as my Primary Server for that account... I do have two 'other' smtp servers showing but they are from other providers (not related to gmail) and both are OFF for my gmail account settings. (If you tap on those other smtp servers, the on/off button is displayed and... at the bottom it should say which account is using that other server.)
- My primary server (Gmail SMTP Server) is using SSL and Authentication Gmail Client Token and server port 465 (the 'secure' SMTP outgoing port)... and all that is 'dimmed' (inaccessible).
- With cellular service off, using WiFi... I am able to send a new email through my gmail account to another of my email addresses, and then... I can reply to it from that other unrelated account which has its own Primary Server (different, not Gmail's).
- Assuming your Gmail password is entered correctly... (the same for the Gmail SMTP Server as for your Incoming server)... I would turn all 'Other SMTP Servers' OFF, and just leave the Primary 'Gmail SMTP Server' "on". (I do -not- have any 'other' smtp servers named 'smtp.gmail.com'... whereas you have shown two, with one of them also 'on'.)
... and then try sending.
- And... Last but not least.. if that doesn't work and you are on the NMMU wifi, you might try adding the NMMU SMTP server (with NMMU account username/password) to 'Other SMTP Servers' for the Gmail account and turn it on (does not have to be primary). Usually, when connected to a local network, access to other outgoing mail servers will be blocked to prevent 'spam relaying'... and then you have to send all email out through the outgoing server of the network to which you are currently connected... (wifi mode).