Whether the intercept matters or not really depends on what your model is trying to assess and what the meaning at the intercept actually is. Often the intercept alone has very little meaning and I wouldn't abandon a model just on a non-significant intercept though (but I also wouldnt abandon any model just because variables were insignificant!).

Your R2 implies that your model describes whatever relationship you are looking at well. I wouldnt however really say that any model is 'significant' just that a model is significantly better than some other model which could be used.

Maybe a bit more information about what the variables in your model actually are would help add a little context.