how to conduct research on data which are not belonging to any particular distribution .can we rely on various non-parametric tests and how we can validate it?
For this you will have to compare with related studies and if it is novel domain then you can conduct interviews to match you data I.e, true picture of data.
Yes we can. For non normally distributed data anyways the right statistical tool to use is the non parametric. So why do you need to further validate it?
It is well know that parametric test (with inferential statistics) are more robust than non-parametrics. If the assumptions of parametric tests are achieved, I will never go to non-parametric. However, in case of Violation of these assumptions, the only alternative is the non parametrics.
If the assumptions of the parametric statistical models not satesficed ( specially normality) you use non parametric statistics, you didn't mention the questions which you trying to answer, but you don't have to validate them.
Although the parametric tests are more powerful as compared to nonparametric test but in case of violation of normality assumption, the non parametric tests are reliable.