1. Sinn Féin constituencies - show me how they're materially disadvantaged.
With a Sinn Fein MP, you have nobody to represent you for reserved decisions. This includes taxation, defence, immigration and security. Pretty important areas. Of course, they will have representation for the day-to-day issues affecting most people that are devolved (schools, health, transport etc). But by not electing a working MP, the voters in these constituencies have no say on these important reserved issues. They have no MP to lobby if they disagree with or are adversely affected by an issue.
That obviously doesn't affect most people - the vast majority of people never meet their MP. But your MP is your contact in parliament, and without one you cannot influence change or raise concerns in the devolved areas. And that deprives citizens of engagement in democracy (although I agree that very few people use these opportunities).
Besides, do you actually think that anywhere is better served by not having an active MP? I'm not talking about individual cases where the MP is useless (see the above lists), but in general do you actually think it's ever better not to have an MP than to have one?
2. Nobody gives a flying toss about Northern Ireland in parliament anyway. British policy is simply to implement the institutions within the Good Friday Agreement and to leave the rest "up to the Irish people". No criticism on this approach, just stating facts. Relevant local NI issues are rarely heard in parliament.
I agree that NI gets little say in Westminster, and it is a disgrace. I completely sympathise with those who want NI to leave the UK (although I abhor the methods of some), as I think they would get a better deal in a unified Ireland purely from a political perspective. (Although this is of course a decision for the people of Northern Ireland to make and my opinion is somewhat pointless and simplistic - I do not wish to get into that minefield!)
The fact that Westminster fails NI is not an excuse though - Westminster should work for Northern Ireland, and electing MPs who actually bother to turn up for work would maybe go some way to getting your voice heard. Westminster can be criticised for not doing enough for NI, but at the same time their MPs should be much more vociferous IMO.
4. Sinn Féin have achieved more through lobbying the government outside of parliamentary structures than they would have gained by sitting with the rest of them.
They would have achieved more still by doing both. They wouldn't have to agree with the process, but if you're elected to serve in it then participate. Alternatively, if you don't to turn up, don't waste your time running for election. They would still achieve all that they would outside parliament, but they also wouldn't be taking up a position that someone else can fill in a much more constructive manner.
It is the opinion of many in NI that Westminster is a total irrelevance, and that includes many loyalists. Parliament has no wish to understand, or get too involved with the province. The best quality candidates in NI parties are usually selected to stand for the Assembly rather than as an MP (with the exception of the new-look UUP perhaps).
See above. Westminster probably is an irrelevance in NI, but that should not be the case. Both Westminster and the MPs elected by NI should act