1 Question: You can ask each of them "Where is the correct door?". It's not a tricky question, so you're safe.
2 of the guards will pick the same door. One guard will pick another door. The correct door is the one that 2 guards pointed to because there are 2 truthtellers.

You can have a velocity that the object moves up every frame, and lower that variable until it's negative and the ball drops. Then change that variable to 0 and have it not decrease again when it hits the ground. That's pretty realistic gravity.
The problem with this is that the object will often skip through platforms and never land 'cause it's going down faster than it can pixel check....
But because this is Axe, it's fast and you'll probably be pausing in your loop. You might be able to set it up by only moving it 1 pixel at a time and changing your Pauses so the fall looks realistic.

I don't think so... List of everything in the source:
I write to two appvars, use some pt-ons, manipulate variables some, use text, get getkeys, pxl-tests, write to 2 buffers, and mess with Fix (but I'm pretty sure it always quits in the right way).
I also use some weird gotos and subprograms.
But it's hard to explain code, so I'll attach it.

Is grouping and ungrouping faster?

The equation variables are back. I've switched from Noshell to zStart, but they're back. When I first started using zStart, it was fine. Then I downgraded from OS 2.55 to OS 2.43 and now there's a lot more errors like the corrupt equation variables and crashes when receiving data from the computer.

So say something is all white on the main buffer and either all black or all white on the back buffer. I want to do a Pt-On() of a sprite to both buffers so the black points are entirely black and the white points of the sprite depend on how it already was.
I also want to use the same sprite and turn on all points that should be white in the main buffer and turn off all points that should be white.
Basically, I want to output a sprite and its exact inverse onto a possible grey background.

So... How do I do a Pt-On() where only the 'on' points are turned on?
How do I make it so it graphs that to both buffers?
Do I need to use two commands, or can I do it all in one command?
And the same questions for Pt-Off()

Not if all 64 squares are accounted for. It would probably be a lot easier to keep track of all squares than to deal with 32 pieces - mainly because of pawn promotion.