Is the electrical box in photo #1 a fan electrical box? Were you unable to attach the fan to the electrical box because the screws were to short? If so, why didn't you buy longer screws?

What is that wide metal thing shown in photo #2? What is the purpose of those slim, angled pieces of wood on either side of the electrical box?

What is the brand and model of the fan shown in photo #3?

Yes, that’s a fan electrical box I put in that has an expanding rod dug into the joists. The wide metal thing is the fan mount “wings” for lack of a better term. That part is meant to attach directly to the electrical box. The wooden shims were put in just to ensure no movement, but the box is solid without them. It’s a harbor breeze builder’s series fan from Lowe’s.

I could not attach the “wings” to the box because their width won’t allow me to get far enough into the ceiling.

Per the instructions, the Upper Mounting Bracket "B" is attached to the electrical box. Isn't the Motor Housing "A", wide enough to cover the Upper Mounting Bracket when that bracket is installed below the ceiling? If so, then you probably just need longer screws than those supplied to attach the Upper Mounting Bracket to the ceiling electrical box. You don't want to extend the electrical box below the ceiling.

In order for the electrical box to perform one of its functions, the gap between metal parts has to be of the order of the typical screw holes in the box, thereby minimizing fire hazard. This includes the box vs. fan escutcheon. So the box should be as flush as possible to the ceiling. This is accomplished by either mounting the support rods appropriately, or building a wood structure between joists that can hold a box above and a box below, with the two boxes connected by an appropriately sized nipple and connector nuts to establish the spacing. All boxes, of course, have to have the cubic inch volume appropriate to the number and sizes of wires going into them per the NEC.

@kaseki "thereby minimizing fire hazard."

Fire hazard?

He can replace the existing fan electrical box with a deeper one such as the Raco 299 or, if the area above the fan isn't blocked by a joist, replace it with a fan brace between two joists.

This box is attached to a fan brace between joists.

Thanks for the tips all!

@wdccruise NFPA = National Fire Protection Association. They don't establish requirements on boxes and covers just to antagonize electricians. Exposed conductors outside their raceways or cable jackets are deemed a potential fire hazard that box and receptacle design is intended to ameliorate. Wire nuts are a particular concern due to the potential to have inadequate twist and torque thereby being a possible arc source. Thus, even when set in relatively non-flammable sheetrock, the allowed box set back distance is limited to 1/4 inch. On wood and such it is zero. The OP's photo looks like wood to me.

Thanks y’all. Longer screws did the trick.

You really should mount the box correctly so that it or box plus extension is flush with the ceiling and so snug to the fan. The result of a spark catching any of that wood on fire wouldn't be good.