Sure, you could use the river water. If you're going to use it for showering, it may be a good idea to pump it into a tank, first. That way, you can let it warm, settle any debris, and treat it with some chlorine before use. Inexpensive pumps are available nearly everywhere. Getting a pump with replaceable parts may be the best. Sand and silt eat up impellers and housings pretty fast.
Tip: If you get a strong enough pump to lift the water up to roof level, you could have a dark reservoir on the roof. A black tank with the sun on it will heat water past the temp fit for showering.
Having a single tank for sinks, showering, and waste is no problem. I have a single tank on my trailer right now.