Translation:The supermarket is making a profit.
I can find 3 examples of idir on Duolingo - they all contain a clear r sound that is not evident in this recording.
Téann siad idir Baile Átha Cliath agus Corcaigh
Idir é agus mé
Tá an moncaí idir glasraí agus sicín
You might want to listen to ag déanamh in another recording to see if that helps:
Níl sé ag déanamh aon obair
It's an example of "cup of tea" syndrome.
English speakers often elide the "f" in "of" in normal speech. In Irish, the "g" in "ag" and the "n" in "an" are often elided too. There is no hard and fast rule - just as the "f" in "of" is sometimes spoken, and sometimes not (even by the same speaker), depending on the cadence of a particular sentence, or the formality of the setting, and it doesn't cause a problem for other English speakers, because we subconsciously "hear" the "f", even when it isn't there, the elision of "ag" and "an" is just part of the normal rhythm - sometimes they will be articulated, sometimes they won't. In a sentence like this, an Irish speaker "hears" "ag déanamh", just as an English speaker "hears" "cup of tea", even when the speaker elides the "f".
De Bhaldraithe used déanamh in his 1959 English Irish Dictionary
To bring in, yield, show, a profit, brabach a dhéanamh; brabach a bheith ar rud. To sell sth. at a profit, brabach a dhéanamh ar rud a dhíol; bheith buaite le díol ruda. To make a profit on, out of, a transaction, brabach a dhéanamh ar bheart gnó.
Dineen doesn't have an equivalent example, but he has plenty of uses of ag déanamh that probably fall outside your understanding of déanamh:
ag déanamh coimhightheasa - "making strange.
ag déanamh ar an gcathair - "making towards the city"
ag déanamh grinn ar - "making fun of"
ag déanamh saoire - "spending a holiday"
Is féider leat brabús a thuilleamh freisin, ar ndóigh.
From school days, only tairbhe [Séadna] was remembered as meaning "profit". Now, I know that Brabús, buntáiste, sochar, proifíd does not exhaust the list of terms that can express this notion. Given that the present exercise is under the heading of Business, the most apt word to use would seem to be proifíd as this term appears in Dineen with the commercial connection specified.
The course uses brabús in the Business skill because that's exactly what brabús means - a "profit and loss account" is cuntas brabúis agus caillteanais, "profit sharing" is roinnt bhrabúis, "operating profit" is brabús oibriúcháin, "profit margin" is corrlach brabúis
My copy of Dineen uses "profit" in the definition of over two dozen words, and it doesn't have any entry for "proifíd" (or proifid).
Your Dineen may be the smaller edition of 1933 which indeed does not mention proifíd. I have this edition, but I also have the full 1953 reprint which, on page 862, does. The complete entry is: Proifíd, f., profit (in commerce); al. praif-, preifid. My 1953 Dineen of course also has brabús But Dineen's comments seem to indicate that there is an element of unfairness attached to this sort of profit. For instance, a brabúsaidhe is defined as one who takes an unfair advantage, a fault-finder, an opportunist. If brabús is now the preferred term to use for "profit" in the commercial sense I am glad to see it as proifíd seems to me to be just English lightly camouflaged as Irish. My real interest lies in the subtle meanings of all the synonyms. I have no idea of when and how they should be used, and, therefore, would have to employ brabús every time I wanted to refer to a profit. I am keen to have this hole in my understanding filled.
I was confused by your dates. There were 2 editions of Dinneen's Foclóir Gaedhilge agus Béarla, the original 1904 edition, and the "revised and greatly enlarged" 1927 edition. You have a 1953 reprint of the 1927 edition. It was also reprinted again in 1965, 1975 and 1979. The original 1904 version is available as a searchable PDF, using Latin type here. After his death in 1934, the "A Smaller Irish-English Dictionary for the use of Schools" was published in 1938.
Bear in mind that even in English "profiteer" is usually seen as a far more negative term than "profit". Dinneen's 1927 entry for brabús only attaches the unfairness to the "advantage" meaning - "gain, profit, advantage, esp an unfair advantage, a weak point, a "catch", an opportunity".
A minor point: the smaller dictionary for the use of schools that I have definitely has the date 1933. It was published in London by Simpkin, Marshall, Ltd. for the Irish Texts Society. This does not, of course, preclude the publication of subsequent editions.
Your link to the 1904 version led me to yet another site that I hadn't seen before, i.e. http://glg.csisdmz.ul.ie/ There really is an enormous amount of material online to help students of Irish a lot of which I was unaware prior to my engagement with Duolingo.
It looks as though "A Smaller Irish-English Dictionary for the use of Schools" was first published as early as 1910, but the Irish Texts Society makes no reference to it on their website, and I can find no information on whether it was ever updated or if it was just reprinted subsequently (there are 1955 "editions" available). The 1938 "edition" was "Published for the Irish Texts Society" in Dublin by M. H. Gill and Son Ltd.