"She intends to listen to the woman."
Translation:Tá fúithi éisteacht leis an mbean.
"Leis" causes eclipsis, which trumps the lenition that would otherwise occur here. Therefore "mbean" instead of "bhean". Similarly for various other prepositions. There is a nice description in https://www.duolingo.com/skill/ga/Eclipsis/tips-and-notes
That's all true in two out of three dialects anyway. However, if you're trying to learn Ulster dialect, this would indeed be "bhean".
In Munster, Connacht and An Caighdeán Oifigiúil, most simple prepositions and an cause eclipsis of the following noun (masculine or feminine), so ag an mbean, ar an mbean, as an mbean, chuig an mbean, faoin mbean, leis an mbean, ón mbean, roimh an mbean, thar an mbean, tríd an mbean, um an mbean.
In Ulster Irish, these constructs use lenition rather than eclipsis, but it is important to note that, unlike the nominative case, both masculine and feminine nouns are lenited - ag an bhuachaill, ar an fhear, etc.
I am a beginner and don't have much business answering, but I will try since there are crickets here in Irish Discussion Land. Look again at the rules for eclipsis. One of the rules is that if there is a preposition followed by the singular definite article, there needs to be eclipsis, which for words beginning with b becomes "mb". So if you just have "an" before bean, you have lenition: "bhean", but since you have "leis" + "an" + bean, there is eclipsis and bean becomes "mbean". The eclipsis and lenition rules are hard for me to absorb and I keep having to go back and look at that.
Like English speakers learning that "color" and "colour" are both correct spellings, but in different dialects, learners should, at some point in their journey, learn to recognize that some of the "mistakes" that they encounter aren't mistakes in other dialects of Irish. "Learn both" is a bit excessive.
No, you don't "usually" use the particle ag before a verbal noun. There are lots of ways to use the verbal noun that don't involve ag:
Táim i mo chodladh
Tá an raidió le cloisteáil
Ba cheart dúinn é a dhéanamh
An bhfuil siad á léamh?
ag+VN is one of the first uses that beginners encounter in a consistent way, because English and Irish both use the present progressive a lot, but the verbal noun is not restricted to that usage.
"present possessive"???? What's that when it's at home?
The "present progressive" is also called the "Present continuous"
You might be mixing up the Irish equivalent for the English verb "have" - tá X ag Y, which combines the verb bí with the preposition ag, but a possessive adjective like mo isn't a verb, so it doesn't need ag, any more than "my" requires "have" in English.