The PLAY button tries to launch the executable BooleanAlpha5.exe which doesn't exist. The correct executable name is Boolean.exe, and the only way to launch it is to navigate to the folder where Steam installed it using Windows Explorer.

Every time I try to make a component, the game doesn't even save any of the parts I've selected. What am I doing wrong?

Out of curiosity, to the dev(s), have you ever played Robot Odyssey? It's a game from my childhood, Apple II was the platform iirc. You had to solve problems using up to 3 robots, each of whose behaviour was dictated by the circuits you programmed them with. It was one of the most ingenious games ever made, and deserves a sequel. You could do worse than using it for some inspiration....

In puzzles with multiple outputs, all outputs are initially labelled "1". The true identities of the outputs aren't revealed until you make a connection to them.

you would need 2 AND gates between A&B and B&C with then go into an XOR gate but there just isnt space for it?