Question regarding lakes and watersheds

[cyanide_baby]

Hi everyone,

I don't know if this is the right place to post this question, but here goes.

I've been working on a fantasy elevation map, and I'm now working on its river network.

I'm not sure what to do about certain topographical features though. What happens when rivers reach lower elevation sections of the map in the real world: do rivers fill those lower elevations until they become lakes and water spills over to flow towards the even lower elevations? I can't find any clear answer about this online.

See the two screen captures below:

One shows the river network (a work in progress), and the other shows the same exact region (with the same river network) with the addition of two lakes located in some lower elevation parts of the map.
+ Is this correct, as in, realistic? Is this how water would behave in such a region?
+ If correct, does it mean that I'm gonig to have to fill all those lower elevation sections with lakes or bodies of water?

Thanks.