The filter and the heating of my aquarium do not work anymore. After trying to solve the problem I've concluded that the only way to solve the problem is to buy a new filter and a new heating. Can my fishes (Xiphophorus Maculatus) stay alive during about 12 hours (the time I have to wait until the stores can re-open in my city) without any filter or heating?
Depending upon the type of fish, it may be possible. Some fish are able to survive in a bit cooler water. However, there are some fish that are extremely sensitive to temperature, for example angelfish are very sensitive, and I don't think they would survive. I have had fish such as guppies and neon tetras that were able to survive for a couple days without a heater. It really depends on the fish. As for the filter, I think they should be capable of surviving for 12 hours without one.
The filter shouldn't matter. A proper setup shouldn't build up anything harmful that quickly. I realize that's a loaded assumption, but with a crazily out of whack bio-load, I doubt even a good filter would keep everyone safe. However, most types of filters do have the added benefit of increasing oxygen exchange. Again, that's something that under most conditions won't rapidly fluctuate if everything else is in order.
However, tropical fish are pretty sensitive to rapid temperature swings. The larger your volume of water (and less surface area), the slower your tank's heat will change. Obviously the closer the surrounding atmosphere's heat to your tank's ideal temperature will reduce risk.
How long the fish can stay without filtration would depend on the the size of the tank and the bioload of the fish. The bioload of the tank depends on the number of fish and the size of the fish. For instance, a goldfish will create more bioload than a guppy.
If you have a large tank and a small bioload. The tank can remain without filtration for many weeks.
As for heating, this depends on the ambient temperature of the room which depends on the season and the location. It is better to monitor the temperature with the help of a thermometer.
Fish, being cold blooded animals, are very sensitive to temperature. Any temperature beyond the acceptable range will affect the fish very fast.