You will definitely not spend a lot of money for music/art/theater (3 of your interests) because concerts/exhibitions and theater plays are still rare here.

But for tennis you can spend money if you go to one of the nice hotel clubs. Ritz is one of the only one to have indoor tennis (a must if you want to play tennis in the summer) and the fee should be around 12 000 for single (to be verified) a year and about 20 000 for a couple (access to tennis, squash, spa, swimming pools...). But you may not need to apply in one of those clubs if the company provides you with a house in a compound with a club (to be checked with them what kind of accommodation they are providing).

As well you say you like traveling and Qatar is very well located for travel lovers (between Africa, Asia and Europe) so you need to take that into account in your budget. You can check prices with Qatar Airways site to have an idea of the budget you need.

But in all if you do not run to buy every new Mac coming out on the market you will be OK with the salary they offer you and even able to save some money.

No tax here but you may want to check what says the German law if you transfer money from Qatar to Germany. My brother moved from Doha to Hamburg and I remember that he had to declare the money he was bringing in Germany but I do not remember the details.