Cailín vs. Chailín vs. Gcailín?
So in Eclipses I was introduced to the word "gcailín" which still means "girl" in English but I have no idea why I say "gcailín" instead of "cailín." And then in Lenition I was introduced to the word "chailín" and basically I have no idea what's happening anymore.
There's also mbuachaill, and gcapall, and bportán, and I have no idea why these letters are added to the fronts of these words. I know there HAS to be a reason...could someone explain this to me? Le do thoil?
So what's happening is you've finally encountered the initial Irish mutations. They were originally for to help pronunciation, but have since become a grammatical marker for many things (such as the past tense).
There are a lot of rules for when to use them; too many to really go into detail here. However, for a fairly clear overview, with examples, I suggest looking at the Gramadach na Gaeilge page on the initial mutations.
cailín, gcailín and chailín aren't different words - they are the same word with modifications to indicate certain grammatical issues.
Pay less attention to the modified noun itself (gcailín, chailín) and more attention to the source of the modification - whether it's a preposition+definite artilce (leis an gcailín), or a possessive pronoun (do chailín, bhur gcailín), or the tuiseal ginideach, etc.