Can mutation ever be blocked by intervening words? I know it's idir fhir agus mhná, is it thus do bhuachaillí agus chailíní, go anois ndeir agus gcreideann sé…, an t-iasc agus t-uisce, etc.?

??? what is this meant to mean?

do bhuachaillī agus chailīnī -> it's wrong afaik. Nowadays people often write and say "do bhuachaillī agus cailīnī" because of the influence of English, but I was taught that genuine Irish would repeat the preposition: do bhuachaillī agus do chailīnī, do Sheān agus do Mhāire agus do Shinéad.

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Is fearr Gaeilg na Gaeltaċta ná Gaeilg ar biṫ eile
Agus is í Gaeilg Ġaoṫ Doḃair is binne

It's supposed to mean: That he now says and believes…

I don't think there's "blocking" but there are a few instances of transferred lenition and even fewer of transferred eclipsis.
E.g. idir fhir agus mhná.
As Lughaidh said it is do bhuachailli agus do chailíní. (idir is an exception to this rule.)

And in the last examples:
go ndeir sé anois agus go gcreideann (sé).
If you want to leave out the subject you do so in the latter verb, not in the first verb as in English.
Go is a verbal particle. It must come immediately before the verb. And it must be repeated
(in case "go" means "so that" you could say alternatively: go ndéarfaidh sé agus creidiúint)

an t-iasc agus an t-uisce

Alright, thanks for clearing that up for me.

One final question about this: does it work the same way with conjunctions? I know "If I don't see him" is Mura bhfeicim é, but is "If, after that, I don't see him or hear from him" Mura, tar éis sin, feicim é nó cloisim de or is it more like Mura bhfeicim é tar éis sin nó gcloisim de?

mura can't be separated from the verb,
Things like "mura tar éis" are impossible.

Alright, so I guess a) that applies to all conjunctions b) the subject and conjunction itself have to be repeated for each verb used?

Yes it has to be repeated: mura bhfeicim é nó mura gcloisim de

In case of má/dá/mura and the conjunction agus, there are other options besides repetition:
má fheicim é agus má chloisim de
má fhéicim é agus go gcloisim de
má fhéicim é agus cloisteáil de

Things like "nó gcloisim" are impossible because there's no reason for eclipsis.

Alright, thanks.