"agus é oscailte" literally means "and it open." This is called a "small clause," which is an oddity of Irish where you can have a subject and a predicate with no verb linking them. You can get them in English more rarely, like "all this food and me with no fork," or whatever. They're everywhere in Irish.
You can't parse this construction that way, you just have to accept it.
agus + pronoun is usually an indication of "temporal coordination" - "when", "while", "during" - the most appropriate translation will probably depend on context.
A few examples from the NEID:
"while he was cuffed" - agus é faoi dhornaisc
"as he drew his last breath" - agus é ar tí síothlú
"now that you mention it" - agus é luaite agat
"during his boyhood" - agus é ina ghasúr
"in his teens" - agus é sna déaga
"when he was young he was a bully boy" - bulaí ba ea é agus é óg
I'm a little confused about when to use "fiú" versus when to use "fiú amháin". I'd written "Fiú agus é oscailte", but that was marked wrong. But I've seen "fiú" used in isolation to mean "even" (possibly more often than not). What's the rule that determines when you have to add the second word. What's the subtle difference in meaning between the two?
agus means "when" in this sentence.
Normally, sentences and clauses in Irish start with a verb. So when you see a pronoun immediately after agus, you know that it isn't a simple conjunction joining two clauses ("and"). Instead it's a more complex type of conjunction, usually expressed with "while" or "as" or "when".
Here are a few examples from the NEID of sentences that include agus é, and some of the different ways that this is translated into English - it's not a simple one-to-one translation:
"here's a photo of her as a primary school pupil" - seo grianghraf di agus í ina dalta bunscoile
"Seán turned up in his bare feet" - tháinig Seán agus é cosnocht
"his dad cleared off when he was young" - ghlan a athair leis agus é óg
"he was caught (as he was) cogging" - rugadh air agus é ag cóipeáil
"he died in middle age" - fuair sé bás agus é meánaosta
"eat your food while it's warm" - ith do chuid bia agus é te
oscailte is an adjective, "open" or "opened":
doras oscailte - "an open door"
intinn oscailte - "an open mind".
oscailt is the verbal noun of the verb oscail, and ar oscailt basically means "in a state of openness", and is typically used where you would use "open" as a predicative adjective - Tá an pháirc ar oscailt.