Sometimes the game is like a perma-death run in Fallout, and I really love it for that.
The +1d6 rules for rivers would, as you could expect, provide the 1HP recovery as they are attached to the lake. Rivers would technically only be placed in adjacent tiles that had not already been revealed. This doesn't stop you from replacing tiles. I left the rules vague there for the player to make a decision that they feel is the best.
Anomalies stay indefinitely. I didn't provide rules for closing them as the risk and reward of going into them was fun to experience. If you feel like your luck is running too high, just place an X over the anomaly location to indicate that it is empty. Anomalies are just metaphysical oddities, so the infinite providing of artefacts is feasible in the world of Courier.