Names might be able to be translated directly, but it helps to know at least a bit for background knowledge. Also, Irish morphological rules like lenition and eclipsis only apply to names when they're native Irish ones, so they probably want us know at least one so we don't think all names are unlenited.
Otherwise, it's just a useful mechanism to learn about verbs, etc. without just the generic pronouns. That's my take on it.
Irish and English both differentiate between the simple present (itheann Pól, "Paul eats") and the present progressive (tá Pól ag ithe, "Paul is eating").
Some other European languages don't make this distinction, but in Irish, itheann Pól does not mean the same thing as tá Pól ag ithe.
Yes - tá Pól ag ithe.
Unlike some other languages, both Irish and English differentiate between the simple present - Itheann Pól/"Paul eats" - and the present progressive (also called the present continuous) - Tá Pól ag ithe/"Paul is eating".
When dealing with Irish and English, you can't translate a present simple statement in one language into a present progressive statement in the other.
Yes, síneadh fada (or simply fada) is the Irish name of the vowel lengthening and of the sign that is put above a vowel to mark it. In English it literally means ‘long stretching’ and when used to refer to the diacritical mark in particular it’s called ‘the acute accent’ in English.
So yes, they’re called fadas. And yes, they’re ‘accents’.