Earth is relatively shaped like a sphere, so maps we have of it generally show on a flat surface (two dimensions) what is actually happening over a whole volume (three dimensions). We don't have to put North at the top of a map, but we need to choose directions in a map to show a world of three dimensions in two.

Historically, other directions other than North have been chosen as "up" by different cultures. One benefit of having North as up is because the magnetic North is near the North Pole. But Earth's gravity doesn't pull us in the direction of the North or South poles; it pulls us towards Earth. If it weren't that way then we might see people fly off into the sky near the poles.

Water flows downstream because of gravity; it moves from higher elevations to lower elevations, which explains why the Nile flows from the highlands of East Africa to the much lower Mediterranean sea.

You are correct that north is up, however it is not always downstream. Upstream and downstream refer to the direction the river flows, and rivers will flow from higher elevation to lower elevation (which is the direction of downstream). The reason the Nile flows north into the Mediterranean Sea is that it comes from a higher elevation in Rwanda to the lower elevation of the Sea. Hope that helps!