Walls – Should I use a screw or anchor bolt to hold a metal box to the wall

If you have doubts about the ability to solidly attache the screen with two screws into the wall, I'd consider putting up a 1x2 or 2x2 strip, then attaching the screen to that.

You should be able to use a number of screws to attache the strip to the wall, and if you're not concerned about removing it you could even glue it. Then you can screw the screen to the strip, which should hold it without any problems.

If you need a completely flat mount for the screen, you can build a frame out of the same material.

There is quite an 'overhang' of the screw (24 mm) from the wall. That's why you need at least 6 mm screws in diameter. It's head is about the maximum you have.

That implies 12 mm anchors, which are 60 mm long here.
The resulting screw would be 6x80, or 6x90, if you have longer anchors.

Remarks:

• the overhang should be as short as possible, that's why you shouldn't push the anchor unnecessarily deep into the wall. Too big lever would strain the screw, the anchor and the wall.
• I'd drill the hole not horizontally, but several degrees (5° - 10° from horizontal line) from top to bottom. It wouldn't let the screw to be pulled out when it settles (lowers its head) a bit.