There is a logical reason. The vowels both sound like a because they are both a. The e and i are not pronounced. They are there to slenderize the l. Every consonant in Gaelic is considered either broad or slender, which affects the pronunciation. If it is slender, as here, it has to have an e or i on either side. That is why there are so many extra vowels in Gaelic. It's like action in English, where the i is silent but added just so you don't pronounce it as Acton. The i does not affect the o and so it is not a diphthong, even if some books say it is.
Okay, there are five vowels: a, e, i, o, u.
e, i are ‘front vowels’, pronounced toward the front of the mouth. Gaelic refers to these as “slender” vowels.
a, o, u are back or mid- back vowels, pronounced farther back in the mouth. Gaelic refers to these as “broad” vowels.
There is a rule in Gaelic that both of the vowels before and after a consonant must be of the same type— so the rule is “broad to broad, slender to slender.”
However, the presence of the front vowels (slender vowels) also affects the pronunciation of the consonant, shifting towards the front of the mouth. (Linguists and phoneticists call this “palatalization”, FYI). That’s what they mean by “slenderizing”.
Does that help?
The problem is that boundaries between categories vary between cultures and over time.
In the past you would have been a child (nighean in Gaelic if female), then you would have been a maiden (caileag, 'young, unmarried woman'), then a wife or married woman (bean). The concept of woman, covering everything above child did not exist. That is why a new word has been introduced with that meaning - boireannach (originally a female thing, hence neuter gender which later became masculine).
My guess is that when boireannach was introduced (which it wasn't in Ireland - bean (pronounced 'ban') became the generic word for a woman in the modern sense) then caileag was somewhat redundant and this led to confusion about what it meant.
Yes you can say it. They cannot give you every valid thing you could say as every single question is written by hand, checked by hand and recorded by hand. There is no Duolingo algorithm generating these sentences.
Although they haven't done it, it would be possible for Duolingo to do this in some languages (the ones with a computerized voice) but not for Gaelic where we are so lucky to have real voices.
So here 'agus' is pronounced with a y sound but in module 2 it's pronounced with the hard g. Which is it now?
True. But it should be noted that the y sound is extremely rare in this word, and even fluent Gaelic speakers may find it odd if you use it. I would stick with the g.
I wouldn't call it "extremely rare" at all. Some people would pronounce agus with a hard g /k/, but I'd say more people pronounce it with a softer gh, as in /ɣ/ or even /j/. Being a sound that doesn't appear in English, it's a hard one to explain to people. Your best bet for pronunciation would be somewhere in the middle of an English G and Y.
When they started making this course they just grabbed any willing fluent speakers they could find for the fairly arduous task of recording hundreds of sentences, so we should be thankful to the speakers' hard work, as well the writers'. However, this one pronunciation of one word is so unusual, and such an odd way to pronounce a g in Gaelic or Modern English anyway that it causes loads of confusion, and it is not really appropriate at the beginning of the course.
Note that I said Modern English. This is because this sound change did occur in Old English, which is why we have some words with a y, such as day where a g is historically correct (German Tag).