I know the rules say that you can't have a red or blue side touching another red or blue side. But can the red and blue "points" line up with other red and blue points?

The points can, yes. But the actual borders cannot be place parallel to each other.

Basically, what you cannot do is have it so that to cross from one tile to adjacent one you'd end up crossing two colored borders. If the tile placement is such that this isn't the case, then it's legal.

You can have a long mountain "chain" depending on how the tiles are placed - that is fine, as long as they never "overlap" borders.