When scoring a river after placing a tile that is a lake with fish will the lake with fish continue to score points as new rivers are extended from it with newly placed river tiles?
Yes. The lake is an end point and will score any of its branches that have another end point (either another lake or a spring). But if it still has open branches, its fish will score for each of those when they close.
In addition, they will score for the Huts at the end of the game too.