Is it permissible to use an old version of a computer program that is no longer supported by the company? And must a Muslim inquire about the origin of a gifted program copy?

There is no objection to using a version of the program for which the company has ceased support. There is no need to investigate and scrutinize the source of money of those one deals with in buying, selling, and gifting. Investigating and scrutinizing that is considered a blameworthy excessive strictness and an innovation in religion. Whatever the Muslim knows to be unlawful, he avoids. Whatever he does not know, he does not seek to uncover. The default is that money is permissible. Sheikh al-Islam Ibn Taymiyyah said that if a Muslim knows that money is usurped or acquired through unlawful means, he must avoid it. However, if its status is unknown, the default is that what is in the possession of a Muslim is his property, and there is no doubt in dealing with a righteous Muslim.