Start with "Half close the laptop - leave it open but not fully" - this is very clear here. Then continue with "A bit more/less closed/open" until it's the perfect angle for you. Alternatively, if you want it nearly closed, you could say "Can you nearly close the laptop lid, but leave it slightly open so it doesn't sleep?" or if you're speaking to a well educated English speaker "Can you leave the laptop lid ajar - not fully closed or open, but nearly closed" Or if you want it slightly more closed than it currently is, but not changed much - only slightly reduced in angle, you could say "Close the laptop lid just a little bit so the angle is less open but not much different to how it is now" ... or if you're speaking to a well educated mathematician you could say "close the laptop slightly so it's at about 15 degrees more acute an angle than it currently is" or "please make the laptop open at a 90 degree angle (a 'right angle') such that the screen becomes perfectly perpendicular to the table and keyboard" As you can see there are many ways to convey the meaning, and they vary depending on what exactly you want and who you are speaking to!

I would say: "Could you tilt the screen in a little?".

I think the word you're looking for is "to narrow".

Sometimes there is no answer to "why?" Languages evolve over centuries. They are what they are. Sometimes the logic is "by analogy." "to close" - analogy between closing a door (on a hinge) and a laptop lid (on a hinge). Let me close the door, then we can talk. Let me close my laptop, then we can talk.

You could say, 'Can you lower the lid a little?' 'Can you close it a little more?' When we add 'a little' it indicates that you don't want it to be closed completely.