as I'm sure you know, the verb deirim was originally adeirim, just as táim was once atáim. Both verbs lost the "a" a while ago, and it appears only in the relative, where the fact that a relative "a" is followed by a verb that originally began with "a" has helped to preserve the "a", and explains why the t and the d are not lenited, as they were not originally the initial consonants coming after the relative.

For this reason, I like to put the "a" and the "deir" together: "Dia dhuit", adeir sé - just as atá is written as one word.

This is also why in some dialects it is: ní deirim - because the d was not initial, being "ní adeirim".

Mar a dúirt patrickjwalsh, is é "adeir" an seana-leagan den bhriathar

Nevermore!

Is "an té atá gan mac" right?

I think "gan mhac" would be better, but apart from that, can you say "táim gan mhac"?

I think - but don't know and I would welcome correction - is trua an té ná fuil aon mhac aige - would be better.