Hello I made Stax, and Stax 2 but I didn't see this before. I'll take a look at it sometime. The double inputs are probably because it doesn't use events, it would need a whole new input system to fix it. What it does it check if the button is currently pressed, so based on the flow of the game (based on timing) it could tick of twice quickly...
As for the pause menu taking a lot of cpu time, I'm not sure, these old games were made for DOS where a busy loop was normal so it needs a better implementation as well probably. I wouldn't expect a fix next week but I do fix bugs in all my games eventually if I have time, but I'm slower than I used to be.