I am having trouble with "Bhí eolus maith curtha agam ar
na bóithribh go léir, a bhfuil tríd an bparóiste dhíobh". Why not "a ritheann tríd an bparóiste"? Is the meaning "roads, by means of which there is PASSAGE through the parish"? Is "tá trí X de Y" a recognized
phrase meaning "you can get to place X via Y"?

"a bhfuil tríd an pharoiste díbh"

Tríd here is throughout, i.e. all the roads in the parish. No direction implied.

trí [réamhfhocal]
ó thaobh taobh, ó cheann ceann (ag gabháil trí Thrá Lí; dul tríd an liosta); polladh, réabadh (chuaigh an chaint trí mo chroí; ag teacht aníos tríd an talamh); ar fud (ag siúl tríd an aonach; tá an teach trí thine); measctha le (cuir ola tríd); ar feadh (tríd an oíche, tríd an stoirm ar fad); mar gheall ar (trí dhearmad a tharla sé) trí chéile i dteannta a chéile, in achrann; buartha tríd id tríd ar an mórgóir.

Aonghus, my trouble is the indirect relative and the dhíbh at the end. If it were: na bóithre atá tríd an bparóiste, then I would get it completely.

a bhfuil * tríd an pharóiste * díbh
what there is * throughout the parish * of them

This is an adjectival phrase (or whatever you grammarians call it) describing bóithre and emphasising go léir.

Thanks, Aonghus - I see now. The "a" is the comprehsive relative particle. I don't know why I didn't understand it, but I expect I will get future occurrences more easily!