The population of the republic is around 4.75 million so in total on the island, there's 6.6 million.
1) A lot more than 100,000 people died due to the famine with most estimates putting the figure at 1 million deaths in total due to starvation and famine-related diseases with about the same number emigrating.
2) I agree with not using emigrated populations and their descendants as a basis for possible population growth but I must say one has to factor in social atavism into the population discussions. For many people, the famine would have hit home the dangers of reaching any kind of 'limit' in population keeping family numbers, while not small, low especially compared to pre-famine even 100 years after said incident. People simply had it subconsciously instilled that a lot of children would be dangerous. I'm not sure of this but I my English teacher in secondary school told us that that same atavism is the reason why Irish parents tend to freak out when their kids don't finish meals.
3)I pretty sure I agree with this but could you explain the reflection more clearly?
Sorry for delay in responding, spent yesterday enjoying the beautiful sunshine on Portstewart Strand!
Re the Republic's population I was startled to find that you are quite right! I had always assumed that we in Norn Iron represented around 25% of the island's population, not 38%. Which does support the view that industrialisation would have raised the population even higher. Even OTL, this would have huge implications if the island even re-unites and would totally overturn the existing political culture and electoral demographics. If you thiink things are East coast centric already...
Re 1) Wikipedia would agree with you (1 million dead, 1 million emigrated) but, if you go to primary sources, such as "Blue books" on statistics, the death rate is noted at around 160,000 people (admittedly that won't include those who died on "coffin" ships). But the 1851 census clearly found that the population had declined by 1.6 million since the Famine. Now there would have been population growth in the three fifths of Ireland not hugely affected by the Famine and that would cover a lot of the deaths, but emigration figures show that in 1845 50,000 people emigrated, in 1846, 100,000 and in 1847 250,000 and then an average of 200,000 people per annum over the next five years. So by 1851 one million people had emigrated (not counting the year 1851 itself where probably at least another 50,000 had left by the time of the census). And the emigration figures don't include people moving to England and Scotland (by the 1870s there are more Liverpool Irish than Dublin Irish) as, at that time, that didn't constitute "emigration". I have never studied that in detail but do know that there was sizeable Irish immigration to Great Britain in the Famine years to (among others) Newport, Whitehaven, Sunderland, Jarrow, Middlesbrough, Manchester, Bradford, Gateshead, Halifax, Leeds, Keighley, Wolverhampton, Birmingham and Glasgow. So, unless you postulate around a million people in Ireland who weren't detected by either the 1841 census or the tax authorities, it is a bit difficult to see where the one million deaths come from. Not trying to be a Famine denier, but I posted an extract from a primary source (which typically I can't now find, I can only see my posts back to around mid 2017 -if you poke about earlier threads on Ireland's economy you may come across it) which put the deaths at under 200,000. Which is still an immense human tragedy of course.
2) I would attribute the freaking out more to the "hungry thirties" than to memories of the 1840s. I remember my father telling me (he had me fairly late in life) about a neighbour man being killed in a mill in Bundoran (whether flour, feed or textile I never learned) in the mid 1930s. He left a widow and several dependent children and the local community quickly organised a collection for them. Although money was scarce no-one was prepared to admit to the fact and everyone gave generously. As my father said very matter of factly. "And that meant we couldn't have meat for two weeks and it would have been three if [his brother] hadn't shot a couple of rabbits". The older generation might not have been enlightened by our standards but they knew tough times and had their virtues as well as vices!
3) A number of factors here including a more calorie efficient rice based diet whereas Irish land is manly best for pasture; also SK is close to Japan (with a population greater than the UK, Belgium and the Netherlands combined, to Russia (with a larger population than Spain, Portugal, Denmark, France and Scandinavia combined) and China (with a larger population than the entire EU) so has a larger potential market for goods and services in its immediate neighbours; moreover SK is a military ally of the USA and has a substantial US military presence; relatively close to the remainder of the Pacific Rim also. Not that Ireland is badly located between Europe and America.