What am I missing?

[Yora]

I can fix the second outflow (the one going by the order) by simple having it start in the forest and not connect to the lake at all, correct?

And can I start the river flowing through the Eleut desert in the mountains?

Yes, both are quite plausible possibilities.

Otherwise, I think the desert and the other open area west of it look a bit too empty. While there are some places where a sand desert directly touches the sea as a sandy beach, that's not a very common thing on earth. I think you could add some small forests or hills close to the coast to offer a bit more variation.
And the other open area needs something There are some huge rather flat plains on Earth, but those are usually isolated from the coast by mountains or at very high elevations themselves. Again, some small hills or forests, and maybe some lakes might provide some variation.

[Lalaithion]

This looks great- I can't wait to see where this goes!