[Latest] -- Why are there two [ice-melting] recipes?

The "normal" ice-melting recipe is considered a chemistry category recipe. I wanted several recipes to be Thermal Plant only, and only Factorio 2.1 allows you to define a recipe as belonging to several recipe-categories. Doing this for 2.0 requires you make duplicates. I also wanted the heat based version of the recipe to work much, much faster, and in larger batches, considering you're working with 500°C heat, again necessitating a seperate recipe.

I should probably use a different icon.

[Latest] -- So which one do I pick in the Signal Picker for auto-crafting?

Its usually a better bet to just supply the final product signal, i.e, [water] or [steam] as you can see in the main page screenshot gallery. That way it auto-picks the correct recipe, and you can also directly measure the amount of produced product by doing smart [Each]-based Decider circuit-nerd stuff, filtered to that very product.

[Latest] -- Plant-2-Plant Heat Transfer is very slow

Yeah, this one puzzles me too. still working out why. While it is slow, it will eventually equalize to the connected heat-network average. Give it some time or use another dedicated heat-pipe connection.