Can sin a-rithist, Iain. Tha beagan Gàidhlig agam.
Say that again, Iain. I have a little Gaelic.
So, I've passed the second checkpoint, and these things are confusing me... how can anyone ''have'' Gaelic?
It's the way it's said in Gaelic. You don't "speak" a language in that sense, the phrase for knowing a language is that one in the sentence, which is usually translated as to "have" the language. In Scotland, when speaking in English, it is usual to say that you "have" Gaelic, in the same way. I think the course contributors want that more literal translation to avoid people being misled into thinking there's a Gaelic word for "speak" in there, which there isn't.
It's certainly true that in Scotland "Do you have Gaelic?" or "Do you have the Gaelic?" is the usual way of asking someone if they speak the language.
See the related comment under the sentence "Tha mi a' bruidhinn Gàidhlig." https://forum.duolingo.com/comment/36961474
That user says he has learned that you can use that sentence to indicate that you know the Gaelic language, but I think that one would be a beginner's mistake that would be tolerated under the umbrella of "We know what you mean."
Normally one would say "Tha mi a' bruidhinn Gàidhlig" in response to the question "What language are you speaking (at this particular moment)?"
Using forms of the preposition "aig" for "having" something (along with why people say "I have Gaelic") was explained in steps in the Tips as you worked through the lessons. On the website, the Tips open if you choose the light bulb icon for a lesson. Here is a link to all the Tips together on one page:
If you scroll through this page, under the lesson "Pets" it talks about having a pet and using the prepositional pronoun "agam" (= aig + mi): Tha peata agam. = I have a pet.
Under Family it talks about using "againn" (sinn + aig) for "we have". And also "an duine agam" = my husband. This shows the use of aig forms for possession (similar to having something).
There is a little bit more on prepositional pronouns with "aig" in the "Home" lesson.
Then (finally) in the lesson for "Phrases 3" there is a summary of the prepositional pronouns with "aig", and also, an explanation for why "Tha Gaidhlig agam" is used in Scottish Gaelic for "I have Gaelic."
Hope that helps!
In fact the same construction in Irish (similar to Scottish Gaelic) even translates to how the Irish speak English: it's not unusual to ask, for example, "Have you any French?", to which the answer would be "I have/haven't."
Then in Irish, to answer the question "An bhfuil Gaeilge agat?" ("have you any Irish?") the modest response is "cúpla focail" — "a couple of words"..