Tá glaeite agam ar an dTiarna, mo chosnamh,
Agus tá éistithe aige liom óna chnuc naofa.

I'm just confused on the words "glaeite" (=cry out?) and "éistithe" (=listen?)

It just seems like both of these words im' confused about are supposed to be function as some sort of verb, yet here it looks like they are being used as nouns. Like "Ta cat agam" is "I have a cat". Can we use the Irish preposition "on me/you/us/etc" with verbs as well as nouns? or is there some sort of verbal noun construction going on here.... Idk much about grammar so hopefully this question makes sense. Thanks in advance.

Something similar happens in verse 6:
Tá codladh déanta agam, agus suan, agus tá éirithe agam, óir do chosain an Tiarna me.

the same thing seems to being going on here with "éirithe" and "codladh déanta", where in the latter case we have two things that look like verbs in a row... Does "Codladh déanta" roughly translate to "lay down"? Otherwise I feel like the word "sleep" appears twice with codladh and suan.

Thanks!

glaeite and éistithe are the verbal nouns: 'called' 'listed'. The construction form of bí (+ subject [or, as the foreign grammarians like to describe it, 'logical object']) + verbal adjective+ form of ag is equivalent to the English subject + have + past participle (+ object), so tá glaeite agam ar an dTiarna lem ghlór = 'I have called unto the Lord (with my voice)', tá éistithe aige liom óna chnuc naofa 'he has heard me from his holy mountain'. If you think about it, the similarities between the constructions tá éistithe agam and tá cat agam are akin that of English (i.e. 'I have heard', 'I have a cat'). Tá codladh déanta agam, agus suan, agus tá éirithe agam, óir do chosain an Tiarna mé = (literally) 'I have done/made sleep (i.e. I have slept), and sleep/slumber (codladh and suan are more or less synonymous), and I have risen, for the Lord defended/sustained me'. Deinim (or déanaim) codladh is more or less equivalent to codlaím, except I feel that the latter has more of an indefinite feel, whereas deinim codladh might refer more to a set 'span' of time (but I'm not a native, so I couldn't say for sure). You're right that 'sleep' somewhat appears twice, but they are two separate words in Irish, so it is somewhat differentiated. You could also think of tá codladh déanta agam, agus suan as tá codladh agus suan déanta agam, literally 'I have made/done sleep and slumber'. Keep in mind that the English version says 'I lie (have lied down, just different verb tenses used differently in the two languages) down and sleep'

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I'm an intermediate speaker of the Corca Dhuibhne dialect of Irish and also have knowledge on the old spelling
Soir gaċ síar, fé ḋeireaḋ thíar