Ok now after some days of trouble I get the solution which works with less work and best for me.
I let the bitcoind running under root, then I called the json-rpi command walletbackup which saves the wallet.dat in the directory which the webserver also uses (/var/www).
The owner and rights for the directory ( and wallet.dat ) I changed with a cronjob over the crontab which is called every minute.
crontab -e // logged as root
insert the following into the crontab file:
* * * * * /bin/chown -R >>your needed username<< /var/www/your file directory
press ESC
type :wq
Thats it.