Perhaps in theory, although transmission losses would be large. But I wouldn't want to be on the mercy of distant countries, perhaps on different continent, for getting energy, especially during winter. And as there are other possibilities than solar energy, I don't see why to go for solar energy instead of the other alternatives.
I am not familiar with the winder conditions in Southern Europe. Is there enough sunlight during winter that it would be feasible to provide a lot of solar energy during wintertime - not just for local use, but to northern Europe as well? It might be that even there is too little sunlight and the solar power would have to come from different continent.
Indeed; though I thought EU had a lot of inter-country grid connections (perhaps more as backups). The distances don't seem outrageous compared to other grids.
Edit: looks like Finland does indeed have international grid connections and imports about 20% of its electricity