Yes, you can save fireworks for the following year safely. It may not be legal to save them where you live, so check your local laws first.
The main points to remember are: Keep them dry, and don't jostle them around much. The enemy of fireworks is water. Even moisture from the air can become a problem, if they are stored for a long time and/or stored in a location with high humidity. The chemical contents inside the fireworks are well-protected by the packaging, but exposed fuses could absorb enough moisture from the air to make them not lightable, and some items like sparklers could take on enough moisture that they won't stay lit.
So, pack up the fireworks well in sealed boxes. If they will be stored for a very long time, or in a location with a lot of humidity, you might consider putting in a packet of silica gel dessicant. That probably won't be necessary if you are only storing them for one year and the box is well-sealed to keep humidity out.
Avoid jostling and banging around the fireworks. This might cause problems by loosening the contents. Rockets with sticks or missles with fins are the most sensitive to this. The rocket engine contains a cone-shaped hollow area, which exposes a large surface area of the fuel, to give the rocket its initial thrust. If rockets are banged or jostled too much, this cone-shaped surface can be ruined and the rocket won't fly. Other types of fireworks are not as sensitive to handling, but it is still not wise to handle them any more than is necessary.
When stored dry, fireworks do not "change" or become unstable or dangerous. I have seen fireworks that were stored for over 50 years perform just as if they were recently made. The chemicals do not deteriorate, as long as no water is allowed into the packages. Heat does not change the chemicals. It takes a great deal of heat to get the firework lit - the high temperature of a lighter is what sets them off, not generalized warmth.
Fireworks which have been stored properly are safe to use and do not become "dangerous with age." If fireworks get wet, they will not be usable. You should soak and then discard those. Do not attempt to dry them out and then use them. Never take apart any fireworks. Only use fireworks which have been stored properly and kept dry and in the same condition they were in when you bought them.
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