"By the will of the people has the Republic's constitutional claim on the North been abandoned?"
No it hasn't - It is still an aim of all the major parties in Ireland.

Please provide a source that shows clearly the clause in the Constitution of the Republic of Ireland that lays claim on the six counties that form the Northern Ireland. You will not be able to do that because that claim has been dropped from the Constitution, correct me if I am wrong but doesn't it take a referendum to change the Constitution? The change came about because the majority of the people of the island of Ireland voted that only the people of Northern ireland had a say in how they were governed and by whom they were governed.

Whether a United Ireland is still an aim of any political party in Ireland is irrelevant, that is merely a political ambition.

"Have the people of Ireland clearly stated their opinion that violence has no place in Irish politics?"
Yes they have

Good pleased to see that we have put that one to bed, so no Republican or Nationalist Terrorist Group can ever claim they have any mandate whatsoever from the people of Ireland for blowing up innocent civilians in order to bring about a United Ireland.

"Have the people of Ireland clearly stated their opinion that it is up to the population of Northern Ireland to determine how and by whom they are governed?"
Some have, some haven't. Those who have are prepared to let give the political process a chance.

Not quite as simple as some have, some haven't, was it Jim. Described more accurately it would be put in the following terms:

The vast majority have, a tiny minority haven't.

As Big Mick says - Live with it.