Not really. The slender r in air is not the same sound as the broad r in ar, but most of us learners don't notice the difference, unless we pay very close attention.
I understood that lenition is adding the letter between the first and second letters as I have, and that eclipsing is adding the letter before the word as in their example. I was wondering why it's written with the letter before the word and not IN the word. What's the difference?
There are certainly instances when ar translates into English as “in”, but I don’t know if a native Irish speaker would think of ar as meaning i (“in”). For example, ar neamh agus ar talamh translates into English as “in heaven and on earth”, but would an Irish speaker think of these two examples of ar as being inherently different from each other?
Are you sure that that was another exercise - the exercises in the Irish course are usually written in An Córas Lárnach, but answers written in Córas an tSéimhithe (primarily Ulster Irish) are usually accepted. That means that both Ar an gculaith and Ar an chulaith are accepted as answers for "On the suit", but the "default" answer is Ar an gculaith.
Yes I'm certain it turned up in 'clothing' as a question asking for "On the suit' as an answer. Going by the date in my wp I encountered it when I first did this skill which was long prior to the big site update, so perhaps it's been edited out by now? I've not come across it again yet re-doing the clothing skill, only 'Ar an gculaith' so far. I'd assumed the questions were bot generated based on user vocab. Is it more basic than that? Randomised calls of pre-written text linked just to the skill section perhaps? It'd be far easier to edit if it's the latter.
There is no reason that it would be edited out (even assuming that that ever happens) and there a number of exercises with actual errors that haven't been removed. If nobody had ever commented on it, it wouldn't show up in a search, but as of now only ar an gculaith and an chulaith show up.
Especially in Connacht Irish, there is very little difference between the pronunciation of culaith and codladh (they might be a bit more distinguishable in Munster Irish, and are quite distinct in Donegal Irish). But ar an gcodladh doesn't make any sense, whereas ar an gculaith does, in any dialect.