Buachaillí is the actual word. In irish, in certain circumstances we use séimhiús (h) eg after mo, do or an. In different circumstances we use úrus (changes depending on the word m for b, n for g etc). Úrus are used after ár, bhúr and a (meaning all of them).
Eg Tá buachaillí ag imirt peile. Tá mo bhuachaillí ag imirt peile. Tá ár mbuachaillí ag imirt peile.
As far as I know, the two other options stand for some modificacions (lenition) produced by certain words before a noun. Since there aren't any here (fortunately, because it hasn't been explained in any lesson yet :P) the correct one is the option with no lenition modification :)
Yes, both Irish and English distinguish between the simple present and the present progressive - indeed it is thought that English may have developed this distinction from it's exposure to the Celtic languages.
Itheann na buachaillí arán - "The boys eat bread"
Tá na buachaillí ag ithe aráin - "The boys are eating bread"
Bhí na buachaillí ag ithe aráin - "The boys were eating bread"
Beidh na buachaillí ag ithe aráin - "The boys will be eating bread"