electrical
I'm trying to install a ceiling fan, however I'm not sure if the electrical box is rated for a ceiling fan. There are no screws available in the box. Am I supposed to use the screws through the box ears and then into holes at the end? The holes at the end only seem to have 2-3 threads, would they be enough to hold the weight of fan? The fan I'm trying to install needs at least 35 lbs weight (actual weight of fan is around 15 lbs). Do I use 10-32 screws or 10-24, and what length?
It would be preferable to know what that bar is secured to and how well. Fans vibrate, and that can introduce a failure mechanism lights (or you), as a static weight, don't have. It sounds like I'd probably use the existing bar if it was my own house, but that's comment, not recommendation.
You have two issues:
Strength of the hickey - Some hickeys are cast from cheap pot metal and would be sketchy. Some are steel but bent in the shape of a U with one open side, also problematic. Heavier cast iron ones with support on both sides wold probably be better.
Strength of the crossbar - Also an issue. consider a heavier duty type or even a full round. Then consider doubling the cross bar up with small bolts joining the pair.
Supplement - In line with other answers and comments, there are real risks installing a fan with other than a properly rated fan box. Perhaps most important is the security of the box itself. The fan depends on the plate, the plate on the hickey, the hickey on the stud and the stud on the box. Is the box well enough attached that it can't be loosened by fan vibration? Also, if the plate is not pulled tight against the box, the fan is balanced on the single point of the extension coming from the hickey.
Best Answer
The label says so, so yeah, it's fan rated
You can see a partially painted over label there that says it can handle a 70-pound fan or fixture when attached to joists that are 24" on center, so yeah, it's a fan rated box alright. However, it appears to use a metal hanger bar running across a joist bay (instead of mounting to a joist directly in the fashion a pancake or saddle box does).
As to what screws to use....
I would use 10-32 screws, about 3/4" longer than the depth of the box (so 2.5" or 3" long) and screw them into the holes in the back of the box that lie behind the cover-plate mounting ears -- they need to engage into the hanger bar behind the box in order to mount the fan correctly, it appears, in your case.