Removing old electrical box in ceiling
At least two of those screws look like wood screws. the other a machine screw. The machine screw probably has a nut on the other end that is spinning when you spin the screw.

In all three cases, try grabbing it (a screw) with a pair of needle nose or regular pliers, and pull down on it while you turn counterclockwise. See it it begins to unscrew. Sometimes you can us a flat bladed screwdriver to apply pressure against a screw while you unscrew it with the right screwdriver.

In either case, as you noted you are installing a fixture rated for a ceiling fan, you will most likely want to gain access to the area above, or open the ceiling a bit further to secure the new mount. (They typically have spikes you are supposed to hammer into the wood, and for good measure holes to make it permanent).

Also, that is obviously some old wire. Just curious, are you going to put in new romex to control the light and the fan separately if the unit you have supports that?

Hope this approach works for you.