Never mind, I actually found an entry for "a" that, I believe, answers both of my questions, haha. If it piques anyone else's interest, here is the entry direct from teanglann.ie: "a7, particle used with abstract nouns denoting degree. (Lenites) How. A ghéire a labhair sí, how sharply she spoke. Bhí iontas orm a dhonacht a bhí sé, I was surprised that he was so bad. Agus a dhaoire a chosain siad dó, considering how dearly they cost him."
It seems like this "a" can be translated as "how" or "so," as an intensifier.
(With poss.a. a) A lán uisce - "much water". A lán daoine - "many people". Mar a shíl a lán againn - "as many of us thought". Is fíor a lán de - "a lot of it is true". Shiúil sé a lán - "he travelled a great deal". Deir sé a lán nach bhfuil sa phaidir - "he says more than his prayers"
The page for a that you referenced also explicitly lists a lán under "a5, poss. a. ... 3. (In certain idiomatic phrases) A chéile - "each other". A lán - "much, many".