Is there some kind of paid service on StackExchange Websites where one can ask a question which will cost him some money, but he will receive an answer no matter how general or basic the question is? And of course this service/answer should be private.
There is to my knowledge no such service.
One of my issues with this is that involving money may give the idea that the quality of answers somehow is magically increased. In actuality, I believe that it decreases as more people would want to answer purely to get at the money, assuming the idea was to pay people to answer. Getting paid does not make your Unix knowledge better or sharper. Paying for an answer does not make the answer better. If everything additionally is done in private, then this totally short-circuits any corrective peer review process.
You should be able to ask questions without paying. If you ask a simple question, chances are that it has been addressed before, in which case the question can be marked a duplicate. If the question is too general, then it's an issue with the question, and no amount of money would make it easier to answer.
I'm not currently aware of one, no.
Kusalananda pointed to a couple posts on the main discussion site, Meta Stack Exchange:
SE paid membership with payout to users who answer questions - asked in 2017 and which was closed as a duplicate of Would it better the community if we got compensated for posts? Even with minuscule alt coins? from 2014.
Offering actual money as a bounty? - asked in 2009 and officially declined in 2011.
There are several answers worth reading in those threads. The votes and discussion there indicate a negative reception to the idea.
Looking at U&L, I found some previous discussion:
- How to deal with 'paid help' questions? - asked in 2012.
- I would be happy to pay real money for succesful solution to my question - asked in 2015.
... both of which echo the "no" sentiment.