You are really going to have a pro come and assess the situation and give you recommendations.

The screw I was referring to would be on the handle. That one you showed is nothing that will help you. However, I can see that there are identifying marks on the mechanism that will help you identify a replacement.

There could be a tiny screw on the handle to tighten it. If not, you probably will have to replace the mechinism...https://www.swisco.com/

https://www.youtube.com/watch?v=hEBjbSTLytk. There are more videos like this.

I does need a bit of a darkened room.

Here's my NXcam projector. Should be the same from everything I looked at. First pic is 9" from wall with a 4 1/2" wide image. Second pic is 25" from wall with a 12" wide image. You can't zoom the projected image. Distance dictates size. I played around with a couple of crappy magnifying lenses and with the right combo and decent quality lens you could throw a little image a lot further. It was upside down but you can always feed it an upside down image and it will project right side up.

Take a look at this. It has a built in focusable projector and all you need to do is put in a card with media. I have a bigger version and the projector works pretty cool. It doesn't have a lot of light output but with your short throw it might be perfect. However, you might need to experiment with some additional lensing to get the image to the right size. You can also use neutral density gels/filters to reduce the light on such a compact area. Definitely doable.

Ok. Let's not play a thousand questions. Pleas describe your idea with details like size, shape, is the image coming out onto something else and if so what and how far. or is it on the surface of the box. The we can give you some thoughts.

Is it a moving image?

You could rub mineral oil on it. Let it sit for an hour and then wipe off.

Ozone is O3. Oxygen is O2. Ozone is always trying to get rid of that third atom by attaching it to something else. That something else that takes that single atom becomes oxidized. Oxidation is a destructive process. Ozone is an air pollutant. It oxidizes lung tissue. Be very careful and do some research on this.