"Ni mor dom" literally means "it is not big for me to". as it is colloquial, is it kind of like a shortened way of saying, "It is not a big deal for me to (do the given task) so I will do it"?
No, ní mór means "it is necessary" or "must". The similarity with "no biggie" is a coincidence, as that doesn't mean the same thing.
I cannot understand any of these verbal sentences - why don't they repeat them - as there's no written help. Especially as the word "ioc" is just being introduced, or did I miss it along the way? also another new word in the previous sentence.. Some written exercises with these new words would be helpful.
It's best honestly to think of it as "It is necessary for me". Ní mór do + prep means "it is necessary for + ". It's colloquial.
Along the lines of "I must" is "I am restricted to" as in "no matter whatever else I may want or intend to do, I still must do this" And so that 'constriction' of arbitrary options also logically explains "Ni mor dom" imo
This will be confusing. As I would think it would be the opposite. So, does "Tá mór dom" mean "I don't have to"?
ní mór dom is literally "not big to me" - so (very) roughly analogous to "not a big deal", but stronger in meaning. Hopefully that should make it clearer.
Not sure about tá mór dom, but I've never seen it and I can't seem to find any examples. You can say "I must" with the future tense of caith - caithfidh mé..., so maybe you could try ní chaithfidh mé... https://en.wiktionary.org/wiki/caith#Irish