What do professors really want in a PhD student in Europe? Background: 
I have done my masters in computer science/artificial intelligence. I want to do my PhD related to data science, applied machine learning. I do not have degree from world's top ranked universities nor I have top quality research publications. I have had some domestic issues since my completion of degree education so I have not been able to fully focus on my career. 
Nevertheless, I am very much willing to learn and upgrade myself is to meet the research labs requirement. With curious mind and life-long learning attitude, I have been doing various online courses (after my work hours)and have worked on different tutorial projects related to data science and machine learning i.e. from text mining, image processing, process mining, genomic data science to blockchain development. 

More background
Since, I want to become a really good researcher and for that Phd is the first step. After my masters, (more than 2 years) I had time to reflect and I take notes about what I am going to do during my PhD. I am going to be a dedicated Phd student where I can work hard, learn, collaborate and produce good quality research publications and build a strong research profile. I am very much willing to learn whatever it takes to complete my Phd project. 
With my qualifications and the skills, I have been applying for PhD positions whose qualification and skills are very much in match with mine. I apply only after I feel confident that I shall be able to handle such project. However, after applying for more than a year, I have not even got reply from most. I have been interviewed 3 times and I have been told that they have found better candidate for the position. One Prof. wrote that he liked my profile and wants to interview but after interview he told me he got better candidate for the position. After one week, I noticed same phd position being advertised again :(. I was interviewed again lately by the same professor, but rejected again. No clue what they really want from a PhD candidate.

My Question(s)

I am really confused about what professor look in a phd candidate? If its the skills and qualification or is it the certain level of interest and passion to go for research degree. I believe, I have both.

What should I do now? Keep looking for PhD positions? Or improve myself (in I do not know what way).

I have been keeping up with my interest for research career even through the tough times. I have applied to more than 50 positions. The only prof. who found my profile interesting rejected me twice in interview. I do not want to give up but do you think I should give up and rather look for other career.

Thank you for your attention and precious time. 
Your feedback is highly appreciated.
Every advisor is different and each wants something different in students they advise. At one extreme is a person with a well established, ongoing, probably funded, large scale project who needs students to do a lot of the research work, leading, one hopes to a lot of papers and doctorates for the students. Their needs are very specific. If you have the skills they need and they judge that you will probably work hard enough (pretty hard) you may find a place in their lab. Unfortunately, the advisor is also likely well known and prominent and so the competition to join the lab can be fierce. If you get in, the work will also be very intense. However, if you can handle it, you will probably wind up at the end with a good, if very intense career for yourself. 

At the other extreme is someone like myself who only ever had a few students and only one or two at a time. I didn't need help on the kinds of research I was doing, other than from colleagues elsewhere, so all I really required in a student was interests similar to mine and the drive to complete the degree with only my advice on their plan and progress. I wanted people with similar interests so that I would be able to give them good advice and so that it wouldn't be impossible for me to judge their progress and completion. 

Anything in between these two extremes is possible. My own doctoral advisor was more like myself than the hard-driven lab master, but he was full of ideas and ran a weekly seminar attended by a few students and also a few other faculty members. He was admired by students and faculty, though he was a bit aloof and very professional. If a student could get over the fear of meeting him, he probably had a problem or two for you to work on and if it went nowhere was able to help you change direction. This seems to me to be the ideal. 

I had an earlier advisor who wasn't nearly as helpful. Part of that was that he was untenured and so spent most of his time on his own research and publications and wasn't able (or skilled enough) to give me much help and direction. 

My advice would be to avoid advisors who are too busy to really advise, either because they have that extremely high powered lab or because they are too new to academia to know what and how to properly guide a student.  Of course, if the high powered option appeals to you, then the superstar prof with the giga-lab may be what you want and need. 

If you arrive for graduate study without already having an advisor, possible in some places but not others, I suggest that you look and ask around for suggestions about who does a good job with students in your field and who does things that interest you. Choosing a compatible advisor may be the most important thing you do as a beginning grad student. 



I should note, I guess, that in some fields you don't really have an option. If you require the Large Hadron Collider for your work, then giga is probably your only option.