Your home is so lovely!! You’ve done such a great job decorating, I agree that this funny light fixture should not limit you!!
It looks like what happened here is that there was originally a chandelier hanging from the ceiling, but when the new light fixture was put in, its ceiling plate was connected to the chandelier’s chain! If it’s possible to get an electrician out to your apartment to remove the chain and attach the light fixture to the ceiling with its actual ceiling plate, that would be a big help!
But there are definitely ways to DIY around that!! You mentioned changing out the bulbs, and that would be a great way to switch up the appearance. Vintage-inspired filament bulbs, especially so exposed, could make for a great impact in the room. Here are some great ones!: http://bit.ly/2cxiSU7
Another option is buy an extra large Chinese lantern and use wire to connect it to the hooks on the top of the light fixture. If you find one large enough (maybe 28 inches?) it could cover the whole thing! Then, if you’re looking for cool ways to update that Chinese lantern, I DIYed some with Maya!