In terms of Belfast's population, it's around 400,000 in the city proper, with about another 50,000 in Lisburn which is only has half a kilometre of Greenbelt between it and South Belfast. The two other termini within a half hour train journey of Belfast, Carrickfergus and Bangor (and the halts in the hamlets nearby), would have around 100,000 residents. As insignificant as Northern Ireland is as a state, it does have a large civil service and you'll find that much of the people that live in these satellite towns travel into Belfast to work in this or other industries. So in a sense as a city it punches above it's own weight in terms of jobs. This is not reflected in the public transport network, which has been under invested in in favour of the motorcar.
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One of the themes I've picked up from reading is that partition had a negative impact on the train network, as around seven of the lines crossed the border (only one of which now remains in use). What they never explain is
why it had this effect. After all the reasons for carrying passengers and goods from one place to another shouldn't change just because the rail network now crosses an international boundary. After all both NI and the Free State shared the same currency, were both nominally part of the British empire, and had a border that wasn't heavily policed- Irish Nationals can still live and work in the UK without applying for visas; people from Northern Ireland can still own Southern passports, etc.
If rail travel between the North & South made business sense before partition then I see no reason why it ceased to make sense once the border was in place. It seems to me that out of sheer political pettiness the Stormont government (and maybe the Dail as well) tried and succeeded in massively stifling communication between North & South.
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In reply to the original poster's second question:-
2. Why were 2/3rds of the network shut down after the 1920s? Is there any movement to bring back these lines?
Ireland was a bit of an oddity in that it probably had a lot more miles of railroad per head of population than mainland Britain did, although admittedly many of these trains would have been cheaper narrow gauge lines. So many of these stations were in small villages that are so insignificant nowadays that they would barely qualify for one bus a day let alone any other form of public transport. Just look at this map of the 1906 network to see how big it was
http://upload.wikimedia.org/wikipedia/commons/e/e4/Map_Rail_Ireland_Viceregal_Commission_1906.jpg
The reason for their existence was usually freight, with passengers being an added bonus. The road network in the Victorian era would have been dire, and investing in branch lines would have been the only sensible way to bring goods to and from these rural and sometimes geographically challenging areas.
But then the internal combustion engine was invented, and there was no longer a rail monopoly. The growth of buses and lorries was initially hindered by the fact that the roads were falling apart and couldn't withstand motorised traffic. But private transport had the advantage of not having to properly contribute to the upkeep of these roads, whereas the railways had to maintain their tracks as no one would fix it for them. So eventually the decision was made by the governments to subsidise road transport by improving the roads. Many of the railway businesses weren't very profitable anyway and with competition from lorries it was inevitable that many of them would die out.
