Because Darksend creates many new adresses for changes, do we have to backup Darkcoin wallet after completion of darksend premix or after sending coin with darksend?
There is a keypool of 1000 keys in a wallet so you have a gap of 1000 sending operations (one mixing round takes few 10s of them). Mixing 100 DRK for 2 rounds can take ~150-170 addresses, for example.
How keypool works: Darkcoin wallet generates 1000 keys on initialization (originally it's 100 for Bitcoin btw). Keys are used one by one but every time you use one address new address added at the end of a list. So at any given time you have 1000 addresses that are already known to you but yet unused. 1000 addresses should be enough in most cases and even after mixing you can open your backup wallet and still will be able to see/move all your coins.
If you feel you that you need more safety you can create new wallet with larger keepool by adding -keepool command line option. If you already have wallet.dat you can move it somewhere else or use -wallet cmd-line option to create another one. So it should be smth like this:
darkcoind-qt -wallet=walletwithlargekeypool.dat -keypool=10000
This will generate new wallet "walletwithlargekeypool.dat" in your data folder and this wallet will always have 10000 pre-generated keys. Keep in mind that this however can take quite a long time to generate (depends on your environment).
I use option keypoolrefill when I'm close to limit and until then I don't do any new backups.