The problem with our country is that we are poor. We need to develop many parts of it. If we begin to think about tamil or sinhala and we start a war along racial lines, no one will get the opportunity to develop the country. Then theres the issue of "look only their areas are being developed" and then people like Prabhakaran will come in and say "that's because you're this race, they are that race, blah blah". That's simply not true. We need to allow each part of the country govern itself, a good solution would be the diferrent districts are given slightly more power to carry on their own projects and govern themselves all controlled by a central government.
What they need to do, after getting rid of extremeists like the LTTE, make sure that by law no one is allowed to use extremeism against the unity and development of our country and it's people. (including hardcore sinhalese extremeists or muslim extremeists, not just tamil extremeists).
For the langauge issue, don't let it be an issue. Already road signs and help is available in all three languages. Allow it to be that way. When people go into Tamil areas where most people in that area are tamil, they will automatically learn enough tamil to communicate, same goes for tamil speakers coming to areas where most people speak sinhalese.
Members of parliament should be allowed to speak in any language they prefer and this language be translated, much like how UN general assemblies take place.
Finally to answer your question, the problems people of the north face, are the same problems people else where face, underdevelopment, bad quailty of life, and easily manipulated by politicians or other organisations because people of Sri Lanka are naturally content by way of culture and at the same time because life is very difficult for the lack of these simple things, people can be shown false hopes and solutions to their problems then taken advantage of.
If we adress these issues everything else will get fixed, because what extremeists use as an excuse to do mad things or use to manipulate people, will be gone.