Ceiling – how to install the mounting bracket for ceiling fan

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.

If your box is that small it is almost certain that it is not a fan rated box. If it is not, then the box MUST be replaced with a fan rated box.

Sorry, but even with approval, someone unlicensed, uninsured, and unqualified SHOULD NOT be doing electrical work in a place that they rent. This is a perfect example; something as "simple" as changing a ceiling fan turns into a project since the box has to be replaced, and in an older house this can be met with issues.