Is there a way how to become a business analyst for software projects without studying in the concrete business domain or having long-time programming experience? Is there some way through education?
By convincing someone who decides on the roles in a team that you can do the job well.
If you don't have any qualifications or experience in the business domain, that means finding someone with low standards, or being very convincing about your ability to learn on the job, or both.
Less ethical alternatives would be lying about your qualifications, bribes, or exploiting nepotism.
A general business degree with a minor in information technology might get you the job without any experience. Moving into the field from either end might be easier.
We have three BAs where I work. Two started in customer support, and the third started as an account manager. None of them are programmers.
To be a business analyst you have to understand the business better than most practitioners as you have to explain it to those not in the business, so I think you do need experience and knowledge in the business domain or supporting the domain.
I think you can become a software analyst without the direct business knowledge if you learn how to produce structured questions (following some form of formal analysis) but you need to learn quickly as most business people I know will stop talking to you as a waste of time if you don't understand them after they explain it a couple of times.
The discipline of software engineering includes software analysis and design, so look for education in that.
Note that you will always be in competition with those who have more business or programming knowledge and you will have to convince people that your analysis is better.
You do not need specific domain knowledge to be a business analyst. The client is generally the domain expert; the analysts job is to extract information from the expert and build or improve a business model and process from that information. However you do need sufficient experience and intelligence to be able to work productively with the domain expert; and no one is likely to employ you simply because you have read a few books on the subject.
I think programming experience is the least necessary requirement for this abstract part of a development process. Most specialist analysts do it exactly because they lack aptitude to interest in programming; and probably have greater 'people skills' than most programmers. For that reason this really is the wrong forum for this question.
There are no doubt local training organisations that you could use; you'll have to look them up yourself for your region. For example Learning Tree International have sites in USA, Canada, France, UK, and Sweden and provide a number of professional development courses in Business Analysis and related disciplines. Some of them are available on-line so can be taken from any geographic location. There are other providers - I know because I Google'd it!