Why is 12's format different than 11, 13, and all the other teens when counting to 100 in Irish?

The Irish alphabet doesn't actually contain the letter H, the H you're seeing is the modern depiction of the "séimhiú" or lenition. It used to be depicted by a dot over the consonant, but more commonly now the letter "h" is used directly following the consonant. Its purpose is to make the word easier and more natural to say, basically. Saying "a dó déag" with the two harsh "d" sounds right after one another is a little awkward, so the séimhiú helps the speaker out by softening the second "d" sound into something that'll flow more naturally from the tongue. If you're interested in learning more, google séimhiú (lenition) and urú (eclipsis).