In answer to the thread title, typically the main reasons why people buy in ireland are:
- UK companies may not take Irish cars as a trade in, so you may have to sell privately
- if you need to sort out a problem or use your warranty, you may have to go back over to the UK (although manufacturer warranties can be claimed anywhere I think)
- cheaper purchase price of UK cars will be reflected in cheaper selling price in a few years time, so don't expect to get value through arbitrage
I did a search on carzone and there are 28 2002/2003 BMW 3 series for under €7k in ireland, albeit some with high enough mileage, so you might even find something you like over here.
Good luck with your search.