Firstly, yes this sentence could be translated using the present perfect (i.e. has lost). Here's a brief explanation of how to translate the Irish past tense.
"My university" would be incorrect here because the possessive m' is before iarratas, not ollscoil (so it's the university, and my application, not my university)
It may mean third level here as well but you would not translate ollscoil as college nor coláiste as university. A college may be a part of a university but a university is never a part of a college. Trinity College is a University: its name is Coláiste na Tríonóide. Coláiste na hOllscoile Corcaigh is University College Cork. This might be confusing for an American but for someone in Ireland this should be straightforward.
Technically that is true, but then the universal colloquial way in Ireland of saying you're attending third level education is that you're going to college, so I wouldn't automatically call it straightforward.
Case in point: the infamous Twitter exchange between Leo and DCU during hurricane Ophelia shows that a fair few Irish people are also still confused ;).