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I lose around 0,75 kilograms per week.

That is a bit high. You will probably lose some muscle. Personally, I believe in slower bulk/cut.

I decided to work out 3 times a week. A workout consists of weightlifting (bench press, squats and other assorted exercises to move every muscle in my body) and an aerobic part when I do stair stepping for at least 45 minutes. The strength training part is for preserving muscle mass and the aerobic part is for losing fat.

Cardio doesn't burn fat per se. All activity burns calories, which helps you stay at a calorie deficit, but it is the calorie deficit that reduces fat storage, not cardio.
Also, there is research that shows that for best results, cardio should always be done in a seperate session, or at least before weight training. Cardio after weights interferes with the very beneficial hormonal response of weight training.

I've kept my heart beat rate in the aerobic range so far but after doing a research in this topic I've been conflicted by the results. I've read that in order to effectively lose fat I need to push my heart rate up to the anaerobic range but some say that it will lead to muscle mass loss because anaerobic exercise needs more energy then my system can can mobilize from burning fat. According to my research anaerobic exercise is important because it speeds up my metabolism and I can keep burning more fat even after the exercise. Aerobic exercise in the other hand only burns fat while I do it.

Higher intensity is almost always better. You don't need cardio for weight loss (unless you like it). Weight training creates the "anabolic" hormonal environment for all the fat loss you need.

So what kind of exercise should I combine to the other part of my workout to burn the most possible fat while losing the least possible muscle mass?

Patience. You are doing fine, you will usually lose some muscle and even some strength when cutting, it is normal. Just keep it slow.

Some tips: http://www.biolayne.com/contest-prep/best-form-of-cardio-for-bodybuilding/
https://www.youtube.com/watch?v=FcM8HablpZk


jp2code:
After about 30 minutes of cardio, your body has burned out of the sugars stored in your blood. Then, it gets energy where it can. That can come from converting fat or muscle to energy.

No, that is why you have glycogen stores...