Iirc the latest version of fMMS and/or fAPN will not show the MMY connection APN anymore in the connection configuration/selection dialo

So to get to the ground:
which version of fmms/fapn ard you using?
are you sure APM settings in fMMS are the same? Especially the proxy setting?
did this happen out of the blue? Or could you receive earlier? When latest?
and so on. Provide as much info you can.

About your question with settings:
It should not throw any errors, as this address is just the base and not a real message address.
I just checked (once more) for vodafone de and here I just get an empty page in browser (as expected). So no idea about t-mob usa, sorry. Someone else from over the sea may check/confirm please?