A tributary
A stream or river called that flows into a larger stream or river is called a tributary.
The stream is a tributary of the river.
The path that a stream follows is a channel.
The bed of the stream.
A stream or brook can get bigger and become a river.
Channel
The path that a stream follows is a channel.
A small stream in a river is called a current.
Ohio River
The middle part of a river may be called mid-stream, mid-river or mature river.
No, a stream is actually smaller than a river.
Tributary is the answer you are looking for, I believe.