It really isn't a good idea unless it is one of each. Since finches are more high strung they will tend to make the parakeets nervous... or make them more high strung. If it is one of each there is a chance they could balance each other out. You could use the same cage but just put a divider net.
No, parakeets and finches in the same cage will result in the death of the finch. Parakeet's like to chew on everything and they will chew on the finches. Eventually the finch will be killed by the parakeet. The parakeet will also rip out the feathers or crush the finch's head.
If the cage is large enough you could put the two birds in a cage together, But you should moniter the birds in the cage to see if ther fighting or stressed out. They would both eat different types of food and need plenty of water. Before doing this I would suggest you contact a professional for more information.
Well... I have a pair of parakeets with a pair of finches in the same cage and they all get along well, but you will need to surpervise your birds the first 24 hours just to make sure they don't pick @ each other. Good luck!!!!