Is money earned from maintaining computers that use non-original software considered unlawful, given that I do not install pirated software myself, and am I obliged to verify whether the software is original or not?

There is no harm in maintaining devices, whether the operating software is original or not, and there is no need to inquire about that because your work is not related to downloading programs. As long as you download programs from an original copy, what is required of you is to advise anyone you know who uses non-original software.