How long can aquarium plants live?

Aquarium plants can stay alive in a bag for around 3 to 4 days. It depends on the type of plant, your climate and the way the plants are stored. Wrap the plants in wet paper towels and keep the temperature stable to help them survive longer

I have an aquarium and I wonder I just put synthetic plants. Can fish survive without plants?

Fish can still survive, it is not compulsory. However, green plants absorb or remove waste produced by fishes and provide useful substance to fishes. If there are no green plants from an aquarium, the waste released from fishes gets accumulated in a fish tank. This accumulation can cause bacterial growth and reduction of oxygen level.