How often do I need to backup my Copay wallet? Is a new backup after every transaction necessary? Is it true that I need to make a backup after each time an amount was sent from a wallet by writing down the 12 words? 

Unfortunately, I had Copay and saved only before the transaction was sent, and now I can not get back the remaining amount.
As long as you did not import any additional private keys manually, you do not need to make a new backup every time. Those 12 words can be used to restore all addresses in your account, past, present, and future.

If you imported any additional keys manually, you will need to make a backup every time you import a key, since they are not linked to the 12 words.