From the comments posted above I understand....
You say that you measure a hot to neutral short at the electrical box for one particular circuit. On the other hand you say that no short is measured across hot to neutral at the outlet boxes.
This can mean one of two things.
(One) Something severed one or both of the wires between the outlet string and the breaker box and in the process caused the two wires to become simultaneously shorted on the breaker box side of the break.
(Two) The shorted pair from the breaker box is feeding a different circuit than you think it is.
For the first case you should really think about what has changed in your building between now and when the outlets used to still function properly. In most cases it is unlikely that wires spontaneously break and short together without there being some interposing disturbance of the wiring. This can give a clue of where to start looking. Did something get nailed or screwed to a wall someplace? Did a window get replaced?
I can think of one case where a wire break/short could happen and that is if there was a loose or high resistance connection that over time caused so much heat to be produced wherein the wires melted apart and also shorted due to the insulation burning off. This type of failure is most likely going to happen inside an electrical box itself where connections exist.
For the second case the obvious thing is that you need to guide your attention to the correct circuit. Note that I have seen many cases where the breaker function labels in the breaker box are incorrect. So double check the circuit carefully.
To aid in either case there is a simple technique where you can run a known good conductor from the destination point back over to the breaker box. Just lay it along the floor / ground. Then wire clip one end of it a wire in question at the destination and use the other end of the wire with your multimeter. This effectively makes one of the test leads of your multimeter long enough that you can look for continuity or opens between breaker box and destination without having to buy other types of test gear. This kind of testing should obviously only be done when all the power is turned off. Use a flash light or battery powered lamp if it gets too dark to see.
One other thing to think about....if not already being done....is that when testing for problems like this it is generally necessary to remove all connections from each wire run and test against wire ends that are free ended.
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.
Best Answer
Since the wire is 14/2, the breaker feeding it must be 15A.
Someone apparently changed that to a 20A breaker (presumably because they were sick of constant breaker trips every time they attempted to use two heat appliances at once). Since that was done, you have the sense of "hey, do it even more".
That "end justifies the means" POV ignores the reason we use circuit breakers in the first place, which is to prevent house fires. The National Electrical Code specifies this based on hard data, and if you're not interested in following that, then this is the end of the answer for you. We can't help you on this site.
Your loads and why they are tripping
A 15A circuit (which you do have, even if it's horribly misbreakered) can accommodate 1800 watts.
A 20A circuit on #12 wire can accommodate 2400 watts.
As you can see, you can run precisely one of these at a time on a 1800 watt capacity circuit (and you get to ignore the refrigerator). A 15A circuit can't handle two.
And you know a second thing: a 20A (2400 watts) circuit can't handle two, either. So bumping the breaker to 20A didn't actually buy you anything useful, it only brought 600 more watts, and that's not enough. Since the 20A breaker is illegal, dangerous and useless, change it back to 15A.
And I bet you didn't know any of this, and were just confused and frustrated by all the breaker trips.
Now, you can make a decision whether you can live with one at a time (refrigerator not mattering) or whether it's worth the blood sweat & tears to bring more power to this room.
More power, please
For a modest power increase, I would bring up 12/3 cable, and wire it as a multi-wire branch circuit. This will yield two 20A circuits (2400 watt each). As we already established, you still can't run 2 things on the same circuit, except,
So now, we can run the A/C, refrigerator and any two cooking appliances.
Bigger please? OK, run two multi-wire branch circuits, for four 20A sub-circuits. Everything at the same time, win!
Bigger still? OK. We'll need a subpanel. The next size up of wire is 10/3 which will give us 7200 -- oh heck, for the same price you could buy 4-wire #2 aluminum for 21,600 watts! Or for less money, #4 aluminum for 15,600 watts, or even cheaper #6 Al for 12,000 watts.
Now your subpanel will have power to spare, and you can give every appliance a dedicated circuit and use them all at once if you want to.
Both options are complicated and require a lot of knowledge, attention to detail and respect for the electrical codes, so best to hire a professional for the job.