Can released prisoners take an examination of institutions, civil servants or engage in public welfare posts?

You can't pass the civil service exam. Article 12 of the Civil Service Law stipulates that civil servants have the obligation to abide by the Constitution and laws. If you have such a criminal record, the political trial will certainly fail.

Under normal circumstances, the political examination of public institutions refers to the standards of civil servants' political examination, so you can't report to public institutions.