As for the battle on the Yalu river and the retreat.
Zasulich was instructed to hold the river as long as he could then retreat. So retreat was the default.
The commander on the theater, Kuropatkin, wasn't the most offensive oriented general. I've read on couple of places he was sure in their own superiority over the Japs, but from these acts I got the feeling he realized they were the ones with handicap, and this made him play it overly cautious. They say he also used the old Russian strategy of neverending retreats with burning everything behind, but he did not abandon Liaoyang without losing a battle. And one part of the scorched earth would be only engaging the enemy when it's depleted (how they beat Charles XII and Napoleon). I read they had awful reconnaissance so good chance he had bad intel or nothing at all.
But back to Yalu. Japs were outnumbered Ruskies 2:1, had better artillery, and managed to cross the river elsewhere where Russians did not expect it. Again bad recon. Probably bad leadership. Holding the line of a river even with subpar soldiers in less number and with worse equipment should have gone a bit better. Maybe they couldn't have won, but delaying the Japs more that was a possibility.