UPS to bypass tripping a fuse?
The fuse is there to prevent your wires from burning up in the walls. A UPS is for a short supply of backup power when the power goes out - not to bypass the tripping of a fuse/breaker. If you're not able to move these loads to different circuits, then you shouldn't use them all at once or allow them to be used together. You don't want to bypass a safety device.

As for your second question to alleviate the problem.. Yes, you should push something off to a different circuit. However, extension cords aren't intended to replace hardwiring not for "on/off" appliances like a heater or refrigerator. Of your situation, I'd say move the computer to a different circuit or extension cord as it's not a huge load.