> Is 'abjad' an old word, found in medieval Arabic grammatical
> discussions? Or is it a newer word?

AFAIK, it is an old word, although I don't know its precise age.

It is roughly the equivalent of English "ABC" or French "abécédaire".

Derivatives from the same root include the adjective <'abjadiyy(un)>
("alphabetic") and the feminine noun, <'abjadiyya(tun)> ("alphabet").

Thre should also be a verb derived from it, meaning "alphabetize" or "sort
alphabetically", but I need to double check this.

Obviously, the word is formed from the first four letters of the Arabic
alphabet (in their traditional order, which is different from the modern one
and similar to that of Hebrew): alif, bâ', jîm, dâl, which are pronounced as
if they were a workd, using the vocalization scheme <XaXXaX>.

It is the first of a set of eight similar (mnemonic?) words of three or four
letter which encompass the whole alphabet:

'abjad(un)
hawwaz(un)
HuTTiyy(un)
kalman(un)
sa`faS(un)
qarshat(un)
thakhidh(un)
DaZagh(un)

(I used capital letters for the "emphatics": in proper transliteration, they
should be small letters with a dot below; the endings in parenthesis are
only pronounced in classical Arabic.)

Hope this helps.

--
Marco