"IRN BRU! Thank you, teacher!"
Translation:IRN BRU! Tapadh leibh a thidseir!
I think we may be looking at the "vocative" case for tidsear. If you address a male person, you lenite and add an "i" before the last letter to slenderize it (Calum becomes a Chaluim). "Tidsear" is a male noun. In this case, I think (won't bet the farm on it!) that since there is already an "ea" the "a" is changed to "i" (rather than have an -eair) and it becomes "thidseir".
That is correct. You raise the interesting question of what to do where there is a diphthong there already. The official rules are horrendous, because of all the possibilities, so I am not giving the list (which I would have to get out of a book). In practice, it is changed to something sensible ending in an i. You will recognise them when you see them, and gradually learn them. D