What is the ruling on saying "Thanks be to Allah and to so-and-so," by analogy with the noble verse: "Give thanks to Me and to your parents," knowing that it is impermissible to say "What Allah wills and what so-and-so wills"?

It is permissible to say, "Thanks be to Allah and to so-and-so," because the verse cited by the questioner (2:172) ("Give thanks to Me and to your parents") supports this. The conjunction used in it is "wa" (and). The prohibition of using "wa" for partnership applies only to cosmic matters related to Allah's Lordship. However, for matters that Allah does not exclusively control without His creation, and which a servant genuinely performs, using "wa" as a conjunction is easy. There are religious texts that support this. Although some scholars believe this has been abrogated, and others believe it is exclusive to Allah's speech alone, there is no harm in permitting its use with "wa." However, out of respect and to avoid disagreement, it is preferable to use the conjunction "thumma" (then).