Ceiling electrical box rated for fan, and type of screws
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.