> Is Dinneen's a good source for helping decide how Modern Irish
> words relate to Middle and Old Irish words?
Yes, it is a very good source. Indeed, I think, it is the best source
for the modern language because the orthography is still the
traditional one. That means, that the spelling is basically the same
as in the old period, only with more glide-vowels and h's inserted -
all of which is predictable, though. The problem with the reformed
spelling is that it is often impossible to foretell how a given
modern word would have looked like in Old and Middle Irish. In the
pre-reform spelling this is practically always possible.
It is clear from the material collected in the dictionary that
Dinneen also included loads of words from medieval sources, not only
from his own time. Therefore it is also an important handbook for
medievalists. And sometimes, like in the case of "teolaide", Dinneen
can even fill out the gaps left by the editors of DIL.
> Should I be looking at Dinneen when I can't figure out
> Old Irish words?
Yes, I can recommend that. I often do it myself.