But I have problems with
the "03 On entering map/not on menu close" thing . . .
It does not have to be subtracted by 1. The reason we use 0x0 in the Value box is because the var starts at 0. The Value box dictates which value the var has to be to start the script. After the script, you set it to 1 (or indeed any other value if you choose to), and this means it no longer equals zero, so no longer activates.
Actually, it overwrites a completely separate number with FFFF, one for which there was no input box (as it was thought to be unused). This is not such a mistake in the tutorial, but for future reference it should always be set to zero, not whatever you set the "Value" box to.
But, I have a question for you. Have you found a way to allow more than one level script (type: 02) activate on a map?